I’m currently running a game in which demons feature as a prominent recurring enemy. Mortals possessed by demons are a thing the PCs encounter on a semi-regular basis, though the possession has been done off-stage in a ritual setting.

In an upcoming session I plan to have the players disrupt a summoning, but would like to introduce the idea that the summoners might try to get the demon to possess a PC by force.

Can anyone direct me to, or propose, a suitable mechanic so that such a thing would represent a form of conflict between two parties other than tradiation combat?

To begin, this sounds fascinating.

Are you using "traditional" D&D demons as your possessors? Certain monsters in the D&D multiverse have abilities similar to what you are describing:

Possession (Recharge 6). One humanoid that the ghost can see within 5 feet of it must succeed on a DC 13 Charisma saving throw or be possessed by the ghost; the ghost then disappears, and the target is incapacitatedand loses control of its body. The ghost now controls the body but doesn't deprive the target of awareness. The ghost can't be targeted by any attack, spell, or other effect, except ones that turn undead, and it retains its alignment, Intelligence, Wisdom, Charisma, and immunity to being charmed and frightened. It otherwise uses the possessed target's statistics, but doesn't gain access to the target's knowledge, class features, or proficiencies.

The possession lasts until the body drops to 0 hit points, the ghost ends it as a bonus action, or the ghost is turned or forced out by an effect like the dispel evil and good spell. When the possession ends, the ghost reappears in an unoccupied space within 5 feet of the body. The target is immune to this ghost's Possession for 24 hours after succeeding on the saving throw or after the possession ends.

However, if you wanted more than just a Charisma save to determine the results of the possession, I would consider using an alternate "battlefield of the soul" for the player trying to fend off the possession, for example, using Charisma or Wisdom as Strength or Dexterity for attacking and having the player have to conjure a mental weapon to defend himself. I'm drawing from the Shadowrun gaming system where "deckers" (hackers) work similarily. I'll see what else I can come up with, but this has certainly touched my interest. Thank you.

I had thought of modelling it off ghostly possession, but as you suggest, I want it to be more of an invisible battle, not just come down to a single roll.

I like you idea of a mental battle. Let a spectral form of hit points be the measure of how long it takes to possess someone. Followed by a possession 'death save'.

Would there be other combat going on around this? If so, how do you integrate the two? Do you sort of "pause" the larger battle while you play out the possession battle? Or do you have them run concurrently (in which case your possessor and possessee are both functionally immobile and out of the bigger fight)? And if the second, can other PCs attacking either barty battling for possession affect the outcome of the battle for possession? Maybe I'm overthinking.

Quote from Maestrino >>

Would there be other combat going on around this? If so, how do you integrate the two? Do you sort of "pause" the larger battle while you play out the possession battle? Or do you have them run concurrently (in which case your possessor and possessee are both functionally immobile and out of the bigger fight)? And if the second, can other PCs attacking either barty battling for possession affect the outcome of the battle for possession? Maybe I'm overthinking.

 I like where you’re going with this. Maybe they should be able to help. Like if one of the PCs want to take themselves out of the meat world fight and enter to help in the spirit world fight. It could add an interesting tactical dimension. Is it better to help defeat the minions and leave the one PC to solo against the possession, or help against the possession and leave the party short handed against the minions. 

Or let the minions help their master at the end of each round, to give the PCs in the real world incentive to kill them quickly. 

I’d be inclined to let them play to concurrently, as part of normal combat, allowing other Perry members to attempt to intervene. 

Right now I’m thinking of the scene from Rick and Morty where Morty is coughing up a giant worm while his family are encouraging him.

You could also go with the "Ghostly" Possession at a lower DC, and then each turn, the PC and the Demon have a contested roll to see who has control. If the demon wins, they have control of the body for that turn. Once either the PC or demon wins 3 consecutive turns, the winner of the possession is resolved.

bragrman, I know this was a while ago, but how did you end up running this?  I'm getting ready for a similar situation with my group now, where battle is happening both internally and externally, with one party member risking demonic possession.