While there is no "touch attack" in 5e D&D, let's walk through how Inflict Wounds works.
Inflict Wounds has both Verbal and Somatic components. Somatic components require:
A free use of at least one hand to perform these gestures. (p. 203 PHB).
The simplest thing to do in the usual case is to drop or sheathe the mace and cast Inflict Wounds, per the spell. Dropping or sheathing the mace costs you neither an action nor a bonus action. Refer to page 190 of the PHB and "Interacting with Objects around you" as well as "Other activities on your turn."
Your turn can include a variety of flourishes that require neither your Action nor your Move.
Since you could draw or sheathe a weapon as one such interaction, dropping or sheathing your mace leaves your hand free to cast that spell.
You can't cast the spell through your mace. You need a free hand ...unless you have the Warcaster feat. In that case, you can cast the spell with the mace in your hand.
You can perform the somatic components of spells even when you have weapons or a shield in one or both hands.
Because you have the feat, you can cast the spell and your Inflict Wounds does the damage ... if you score a hit. That spells requires that you roll for a hit. (See page 205 of the PHB). It is described as a melee spell attack on page 253 of the PHB.
On a hit, the target takes 3d10 necrotic damage.