No, that sentence structure is archaic and no longer used. It is only found in older literature (from around four hunded years ago). Your first sentence is expressing the equivalent of the idea that today would be said as : "If you are not my father, then I don't have a father." The only possible modern usage would be in poetry. Your sentence is incorrect. If you want the proper archaic structure it would be : "I will do nothing if you be not here." or " I will do nothing if you not be here." Nobody would ever say this, however, we say : " I won't do anything if you're not here."

I will do nothing, AN you be not here. Perfectly correct 400 years ago.

See this quote from Shakespeare: "...God save the king! although I be not he; And yet, amen, if heaven do think him me." Grammar vocabulary and syntax are very different in older forms of English. ".... although I am not king, and yet, amen, if heaven (God) thinks I am." would be a modern way of writing it.

You are attempting to produce a first conditional sentence. The clause with "if" uses a verb in the present simple tense, which for "to be", means either am, is or are. In this case, "you are". e.g. If you help me, I will give you chocolate. Your sentence feels odd and the meaning is a little unclear. I think you are talking more about theoretical logic (and not a specific situation), in which case a zero conditional sentence would be appropriate e.g. "If you are not my father, then no one is".

I will have no one that I can consider as a father if it is not you.