In the Unearthed Arcana article "Prestige Classes and Rune Magic" (pdf link), they introduce the idea of prestige classes, a class with only a few levels and more multiclassing prerequisites, borrowed from earlier editions.
I decided to have a go at creating a prestige class based on one from 3.5e, the Red Wizard (note that my knowledge of 3.5e and the Red Wizard prestige class comes exclusively from Neverwinter Nights 2; here's a link to their implementation of this prestige class in their video game).
Given that I only have experience with 5e outside of that video game, I hope that I've translated it to 5e adequately. I've also researched into the 3.5e version, and found that there's something called Circle Magic, which appears to raise caster levels. I wasn't sure how to apply that directly to 5e, so I instead modelled it off of the sorcerer's Metamagic feature, but with restrictions so that it isn't just stealing the sorcerer's thunder.
Are there are any major balance concerns with it, and does it still match the flavour of what this prestige class was going for in 3.5e?
I've attempted to balance the first/second level features that give you +1 to spell related d20 rolls by bringing back the old arcane school restrictions (since Red Wizards apparently have extra restrictions in 3.5e, I thought it made sense to add one here), and giving wizards a sorcerer's Metamagic without multiclassing's spellcasting problems should hopefully be offset by the fact that you have to decide ahead of time, unlike the sorcerer who can do it whenever they like to whatever spell they like.
Anyway, here is the prestige class description, and anything in italics is my commentary on something, rather than a proper part of the description.
Prestige Class: Red Wizard
(I'll include some descriptive text here, probably mostly borrowed from here) $$ \begin{array}{c|l} \textbf{Level}& \textbf{Features} \\ \hline \text{1st} & \text{Spellcasting, Enhanced Specialization} \\ \text{2nd} & \text{Specialist Defense} \\ \text{3rd} & \text{Circle Magic} \\ \text{4th} & \text{Ability Score Improvement} \\ \text{5th} & \text{Improved Circle Magic} \\ \end{array} $$
Prerequisites
In order to advance as a Red Wizard, you must meet the following prerequisites (in addition to the multiclassing prerequisites for your existing class):
- Race: Human. Only humans are allowed to join the ranks of the Red Wizards.
- Class: Wizard, with an Arcane Tradition from the Player's Handbook. Red Wizards focus their studies on one of the eight known schools of magic.
- Alignment: Any non-good. Red Wizards are known to be morally questionable slavers, demonologists, and magical experimenters, and often received support from demons, devils, and drow.
- Character level 5th. Red Wizards only accept those who are already dedicated to and have experience with studying a school of magic.
- Proficiency in the Arcana skill. Red Wizards only accept those who are already experienced in matters of the arcane.
- Intelligence 16. Red Wizard only accept the brightest into their ranks (I know this seems somewhat redundant, but I was thinking of a multiclassed character who just have the basic 13 INT to multiclass into wizard; I wanted this to be more wizard-oriented than that, but without just outright banning multiclassed characters).
- Appearance change. If you had hair, your head is shaved and have red wizard tattoos applied to your bald head upon taking your first level in this prestige class.
Class Features
As a Red Wizard, you gain the following class features:
Hit Points
Hit Dice: 1d6 per red wizard level
Hit Points per Level: 1d6 (or 4) + your Constitution modifier per red wizard levelProficiencies
Tools: Alchemist's supplies
Saving Throws: None
Skills: NoneEquipment
When you take your first level in the red wizard prestige class, you gain some red wizard's robes.
Spellcasting. When you take your 1st level in this prestige class, it counts as a level in the wizard class for the purposes of learning and preparing new spells. For example, if you are a 5th-level wizard, when you take your 2nd level in this prestige class, you would be able to learn and prepare spells of a 7th level wizard, which includes adding two new spells of 4th-level to your spellbook.
Enhanced Specialization. Upon becoming a red wizard at 1st level, you become even more skilled at casting spells from your chosen school of specialization. You gain a +1 bonus to your spell save DC and spell attack bonus when casting spells of your chosen school (as per your Arcane Tradition), but you can no longer learn spells of the opposing school of magic (see this Q&A for a table of opposing schools of magic, specifically the "Direct Opposition" from KRyan's answer). You may still cast spells that you already know from that school of magic.
Specialist Defense. At 2nd level, you gain a +1 bonus to your AC and saving throws against spells of your chosen school.
Circle Magic. Starting at 3rd level, you learn two metamagic options as outlined in the sorcerer's Metamagic class feature. At the end of a long rest, you may apply these metamagic options to your prepared spells, either one metamagic option to two of your prepared spells, or both metamagic options to one prepared spell.
When you cast these spells before the end of your next long rest, you may chose to cast the it using the previously applied metamagic. If you chose to apply both metamagic options to one spell, you must choose which one to use on that casting. Once that spell has been cast in this way, you must reapply that metamagic at the end of your next long rest.
Improved Circle Magic. When you reach 5th level, you learn one more metamagic option and the number of spells you can apply your metamagic options to increases from two prepared spells to three prepared spells. You must otherwise still follow the restrictions outlined in the Circle Magic class feature. (Is this enough for the capstone? I was otherwise thinking of changing long rest to short rest, but that might make it too powerful. Other thoughts were learning two new metamagic options, but still only being able to apply three of them per long rest.)