(1) Never 'at'. (2) Using 'in' or not using 'in' have two quite different meanings. Believe me = trust that what I am saying is true. "believe me, I really did see her kiss him". Trust me = have trust in me. This can include 'believe me' (verbal) but is more general. "Trust me, I will catch it". 'Believe in me' and 'trust in me' are similar. They are more general still. They mean 'trust that I will do what needs doing'. "Boss - believe in me. You don't need to keep checking up on my work". I hope this helps.

I would use 'Trust me' if I want someone to believe something I say. I would use 'Trust in me' if I want somebody to have faith in me and my abilities. I would use 'Believe me' if I want someone to believe something I say. I would use 'Believe in me' if I want somebody to have faith in me and my abilities. Both are similar but they are the differences! I would never use Belive/Trust at me.