the sentence formation is incorrect.

Yes, we shouldn’t start a sentence with “And” but the sentence was in quotations, which means that in the story, “mom” actually said “And how are you doing?” Its ok to be ungrammatical when we’re writing verbatim rite? Or isn’t it? (or is this a question?)

“And how are you doing?”, my Mother asked.

You are using ‘mother’ as her proper name so it needs caps, and a coma needs to come after the quotation…. no need for caps after the quotation of the word, ‘my’.

you do not have a period on the second one and you don’t need caps on “My”

you should not use AND to start a sentence/question.

“And how are you doing?” my mom asked.

here is the way to word that sentence

My mom asked “and how are you doing?”