So I have a campaign where there is an evil npc who is  posing as an ally I want one of them to mistrust him and one to mistrust the one who doesn’t trust the npc but have them not know for sure that someone is bad but still be suspicious of the others

You cannot make your players have their characters act a certain way.

Furthermore, it sounds like you have written the RP before it has happened -- don't try to force a certain type of RP on the players. It never works, and they will find every possible way of thwarting you. Instead, put them into situations and see what happens.

OK so this evil NPC is an ally to one. Go ahead and have him act evil when the ally player isn't there, good when he is there, to seed the idea. But if the players don't bite, they don't bite.

Frame challenge: I think you should try to make the characters mistrust each other, with the help of the players.

GM: Hi, players. This game, we are going to do something different. We are all going to conspire against your characters.

Ok I’ll consider your suggestion and am open to more.

Yeah, you can set it up so that might happen, but you cannot, and should not, depend on it happening.

Having the NPC belong to a faction that one of the PCs belong to can make them predisposed to trust. I had a pretty obviously shifty NPC, but he was from the same cult as one of my players and used his symbols and phrases. The player tended to believe he would get good treatment from this NPC.

In real life, this can be accomplished by passing secret notes to players. I am considering using this technique to breed suspicion and doubt in the party without requesting it or pre-writing it.

So, for example, you can have the NPC move over to where player A is sitting, and then pass player A a note. The note might simply say "he sits down next to you. do not tell anyone the contents of this note." The other players will see the note and think it's important. Keep it up and they'll start to suspect something is going on between the NPC and the character.

Then perform the same ritual with one other Player B, but have the notes actually matter. Player A is now wondering if Player B is getting other mundane notes. Players C & D are wondering why players A & B are getting notes from the NPC.

Then, when the NPC turns out to be evil, the characters are faced with a challenge of deciding what to do when players A & B have been receiving notes from him.

Firstly, I would definitely reframe this to trying to make the PCs mistrust one another, not the players. If the players mistrust one another, I think it likely the game will go south pretty quickly.

Secondly, have a think about if you really want to try to coerce this situation. For one, it is not guaranteed to work, and so you need to make sure your story line can cope if the players don't "bite". It is also a dangerous tactic which could, as mentioned above, lead to PvP and the breakdown of the game.

Keep in mind you only get to pull the “Allied NPC is actually a villain” once. After that, your players will be skeptical of every nice NPC they encounter. This is such an overused idea in D&D, they may not even bite the first time. 

Please be wary of this.  I inadvertently had a group begin to be unsure of each other over how they were dealing with an item based on ONE PHRASE one of the characters used. This led to a blow up and one player leaving. Division within a group can suddenly go unseen ways and be bad if not closely watched.  Just a warning from my experience.

Matt Coleville's advice is actually to just have a nice NPC be exactly what they seem to be (e.g., a nice, helpful druid). Players, knowing they are playing a game, will naturally mistrust someone who is selfless, doesn't seem to want anything from them, and appears, on the surface, to have no ulterior motives. They will assume the DM is trying to pull a fast one and will be intensely wary of the nice NPC.

On the flip side, they will more likely trust an NPC who is overtly unpleasant -- the head of the thief guild who asks for work doing shady stuff in exchange for a little information, and warns that he has assassins on the payroll who deal with those who cross him, is a known quantity that the players will take at face value. Unlike the helpful druid who does favors for them without asking anything in return, of whom they will immediately become suspicious.

Im trying to make my players mistrust each other

No, you’re not. If you make the players not trust each other, then your game (and possibly friendships) will fall apart. You’re trying to make their characters distrust one another. The players are not their characters.

I read people interchange “player” and “character” all the time and it drives me nuts.

Quote from Vulgrats >>

So I have a campaign where there is an evil npc who is  posing as an ally I want one of them to mistrust him and one to mistrust the one who doesn’t trust the npc but have them not know for sure that someone is bad but still be suspicious of the others

 There is no way to make people play the way you want them to play. 

Like others have said it's a really bad idea to have players no trust each other. It's even a bad idea to have PCs not trust each other. That kind of drama only works in the movies, at a gaming table it is self destructive.

Quote from Wysperra >>

It's even a bad idea to have PCs not trust each other. That kind of drama only works in the movies, at a gaming table it is self destructive.

 It really depends on how well your players can separate themselves and their own personal feelings from their characters and their characters’ feelings. It generally takes a lot of active participation from two people who genuinely do trust each other.

Ok