He doesn’t trust me cause his ex was a liar?

I hate when someone takes out things they ex did on the next person they talk to. I think imma distance myself from this guy cause he going joke around about my whereabouts last night like I was lieing and then tell me hates lairs so I screens shot my work time in and out to prove I wasn’t lieing. But I might have to cut him off cause I don’t feel like explaining how this can lead to horrible behavior: me constantly having to prove myself and I really liked him too he was good looking nice and I was very attracted but idk about always proving I’m not lieing.