Quoting to part

Let's say you want to quote part of the sentence that contains two independent clauses separated by a comma. What's the procedure if you want to quote the first half? Do you include the clause-separating comma before closing the quotes? Do you insert an ellipsis? What if you quote the second half and you are opening with the quote, i.e. the first letter needs to be capital? Do you do one of [Y] those parenthesis around it?