Manager who appears not to trust him
I write to seek advice on a supervisor who does not trust and always want to find faults. I work with an immediate supervisor who has no leadership quality, he always wants to dwell on just one simple mistake I once made. I worked with him for the past 5 years, for this past year I have worked with him he has never recommended me for any increment or promotion.

Why does he dwell on the mistake you made? He probably feels the matter is not resolved, you have not admitted the mistake and demonstrated you have learnt from it. Perhaps you could initiate a discussion about the error you made, admit the error, own it, show you have learnt from it, and perhaps he will not mention it again
One of you has to break the deadlock. So, let’s look at some ways to rebuild trust
You need to regain his confidence. Perhaps you can do this by excelling at everything you do, go the extra mile, particularly in the area where you made the mistake that you refer to.
One way to build trust is to be generous and forgiving with others. Being judgemental about his leadership ability will not be helpful. You need to respect each other’s abilities, and understand him, before you judge
You can’t force others to trust you, but you can make yourself worthy of trust and create a more trusting workplace