Can anyone tell me what firearm make and model this is? Thank you

Lakestone

Ricci.Wright

STI??

rufe-snow

I think Ricci nailed it. It's a STI Staccato, or one of it's variants. They make a bunch of different ones, on a semi custom basis. If you got the money, they will be happy to oblige. The one in OP's photos, might be quite different from the standard models. Can't tell because of the holster?

chiefr

Take out of holster and repost to be certain