It's hard to tell
Throughout the editions of D&D, Mordenkainen has been associated with all sorts of schools of magic. Firstly it is important to note that Mordenkainen is an expert at almost all forms of arcane magic. The Epic Level Handbook of D&D 3e says:
Mordenkainen knows hundreds of spells, many of which he researched himself... He knows
all the wizard/sorcerer spells in the Player’s Handbook. As new spells are researched by other mages and come into circulation, Mordenkainen is not slow to discover and pen them into his own vast library of spellbooks.
It is clear that Mordenkainen has vast enough knowledge that he could rival any specialist in their field. That being said, we can look at various publications to get an idea of what types of spells Mordenkainen values/focuses on.
1st Edition
In the 1st Edition era, Mordenkainen showed up in many books, but the one I want to focus on is Mordenkainen's Fantastic Adventure, an adventure module where Mordenkainen is presented as a pre-generated character, a level 12 magic-user:
Spells Known All of Levels 1-6
[...]
Spells Carried
Level 1: Charm Person, Jump, Magic Missile, Protection from Evil and Good
Level 2: Continual Light, Locate Object, Ray of Enfeeblement, Web
Level 3: Dispel Magic, Fireball, Haste, Slow
Level 4: Fire Shield, Ice Storm (x2), Wizard Eye
Level 5: Monster Summoning III, Teleport (x2), Wall of Force
Level 6: Globe of Invulnerability
As can be seen, even at Mordenkainen's earliest appearance, he had access to all spells he was capable of casting, but if we break down the spells he had readily available based on this list, we get this breakdown:
\begin{array}{c|c}
\text{School} & \text{Count} \\\hline
\text{Alteration} & 7.5 \\\hline
\text{Evocation} & 5.5 \\\hline
\text{Abjuration} & 3 \\\hline
\text{Enchantment} & 2 \\\hline
\text{Conjuration} & 1 \\\hline
\text{Divination} & 1 \\\hline
\text{Illusion} & 0 \\\hline
\text{Necromantic} & 0
\end{array}
This suggests that even though Mordenkainen could use all spells, his go-to list at the time focused primarily on Alteration (which later became Transmutation) and secondly Evocation.
3rd edition
A much older and more powerful Mordenkainen made an appearance in the 3rd edition supplement Epic Level Handbook where he once again knows just about every spell. In this case, however, we don't get a basic list of spells that Mordenkainen typically prepares. That being said, this Mordenkainen has epic spells which have to be chosen rather than prepared, of which he has chosen:
Epic Spells Known: epic mage armor, greater spell resistance, let go of me, ruin.
One of these is a conjuration spell, and three are transmutation spells, once again lending the idea that Mordenkainen favors transmutation spells.
5th edition
By the time 5th edition rolls around, Mordenkainen has lost a bit of power after certain events that I wont spoil since they consider multiple adventure modules. However, Mordenkainen is basically reduced to a generic archmage. The spell list we are given for him in his first appearance in 5e is as follows:
Cantrips (at will): fire bolt, light, mage hand, prestidigitation, shocking grasp
1st level (4 slots): detect magic, mage armor, magic missile, shield
2nd level (3 slots): mirror image, misty step, web
3rd level (3 slots): counterspell, fly, lightning bolt
4th level (3 slots): Mordenkainen’s faithful hound, polymorph, stoneskin
5th level (3 slots): Bigby’s hand, cone of cold, scrying
6th level (1 slot): true seeing
7th level (1 slot): Mordenkainen’s magnificent mansion
8th level (1 slot): mind blank
9th level (1 slot): time stop
Ignoring cantrips (since those can't be prepared), we get:
\begin{array}{c|c}
\text{School} & \text{Count} \\\hline
\text{Abjuration} & 5 \\\hline
\text{Conjuration} & 4 \\\hline
\text{Evocation} & 4 \\\hline
\text{Divination} & 3 \\\hline
\text{Transmutation} & 3 \\\hline
\text{Illusion} & 1 \\\hline
\text{Enchantment} & 0 \\\hline
\text{Necromancy} & 0
\end{array}
This distribution is quite a bit more evenly spread than the 1st edition list, but with a favor for Abjuration spells. Granted, the events that led to this weaker version of Mordenkainen also had dramatic effects on his memory and personality, so it is possible that his focus may have changed as a result.
Invented Spells
Another way to think about Mordenkainen's specialization is to look at the spells he has invented. These spells include (I've excluded the prefix "Mordenkainen's" for brevity):
\begin{array}{c|c}
\text{Spell} & \text{School} \\\hline
\it{buzzing} \text{ } \it{bee} & \text{Conjuration} \\\hline
\it{capable} \text{ } \it{caravel} & \text{Conjuration} \\\hline
\it{celerity} & \text{Alteration} \\\hline
\it{defense} \text{ } \it{against} \text{ } \it{lycanthropes} & \text{Abjuration} \\\hline
\it{defense}\text{ } \it{against}\text{ } \it{nonmagical}\text{ } \it{reptiles}\text{ } \it{and}\text{ } \it{amphibians} & \text{Abjuration} \\\hline
\it{disjunction} & \text{Abjuration} \\\hline
\it{electric}\text{ } \it{arc} & \text{Evocation} \\\hline
\it{encompassing}\text{ } \it{vision} & \text{Alteration}\\\hline
\it{faithful}\text{ } \it{hound} & \text{Conjuration} \\\hline
\it{faithful}\text{ } \it{phantom}\text{ } \it{defenders} & \text{Summoning}\\\hline
\it{faithful}\text{ } \it{phantom}\text{ } \it{guardian}& \text{Summoning}\\\hline
\it{faithful}\text{ } \it{phantom}\text{ } \it{shield} \text{-} \it{maidens} & \text{Summoning}\\\hline
\it{force}\text{ } \it{missiles} & \text{Evocation} \\\hline
\it{involuntary}\text{ } \it{wizardry} & \text{Enchantment/Necromancy}\\\hline
\it{lucubration} & \text{Alteration} \\\hline
\it{magnificent}\text{ } \it{mansion} & \text{Conjuration} \\\hline
\it{penultimate}\text{ } \it{cognition} & \text{Alteration} \\\hline
\it{private}\text{ } \it{sanctum} & \text{Abjuration} \\\hline
\it{protection}\text{ } \it{from}\text{ } \it{avians} & \text{Abjuration} \\\hline
\it{protection}\text{ } \it{from}\text{ } \it{insects}\text{ } \it{and}\text{ } \it{arachnids} & \text{Abjuration} \\\hline
\it{protection}\text{ } \it{from}\text{ } \it{slime} & \text{Abjuration} \\\hline
\it{sword} & \text{Evocation} \\\hline
\it{trusted}\text{ } \it{bloodhound} & \text{Conjuration} \\\hline
\end{array}
This gives us the following distribution:
\begin{array}{c|c}
\text{School} & \text{Count} \\\hline
\text{Conjuration/Summoning} & 8 \\\hline
\text{Abjuration} & 7 \\\hline
\text{Alteration} & 4 \\\hline
\text{Evocation} & 3 \\\hline
\text{Enchantment} & 0.5 \\\hline
\text{Necromancy} & 0.5 \\\hline
\text{Divination} & 0 \\\hline
\text{Illusion} & 0
\end{array}
As you can see, among the spells Mordenkainen invented, he definitely showed favor towards conjuration, but I'd say more so abjuration. I say this because many of the conjuration spells are abjuration-like in function, and the most powerful spell Mordenkainen invented, Mordenkainen's disjunction, is an abjuration spell.
Conclusion
Overall, it is clear that, over the years, Mordenkainen has primarily focused on the Schools of Transmutation and Abjuration when it comes to spells prepared and invented. I would wager that these two schools are the ones Mordenkainen is most familiar with and has the deepest aptitude for.
All that being said, because Mordenkainen has been such a wide-ranging spellcaster in the past, it is unclear whether this favoritism is actually a demonstration of higher skill, or just a manifestation of spells he prefers. After all, someone as wizened as he (having known just about every spell a wizard can), isn't really lacking in any school.
Another thing of note is that Mordenkainen seems to disfavor necromancy and illusion magic across just about all of his appearances. This doesn't necessarily mean he is unskilled with this type of magic (as we know he has many spells of this ilk in his repertoire even if unprepared). I just found it interesting to see.