can vampire have a offspring?

Depends on what vampire lore you reference. The vampires in Vampire Academy, Blade, Van Helsing, and Twilight all can produce children. (NOTE: I don't mean change humans and call them children, I mean females get pregnant, carry, and birth actual vampire/half-vampire babies.)

Every vampire book, movie, t.v. show, and cultural lore is different. There is no set rule for what a vampire can and cannot do.

Well, techinically, yes. The people they turn are their children.

But the normal human way, no. Their bodies don't work that way, and their little swimmers would be dead.

depends on their vampire species

According to Middle- and Eastern European folklore, human and a vampire can have an offspring called dhampir. He (?) is usually especially talented vampire-hunter.

yes in twilight breaking dawn part 1 edward & bella had a child

No. Vampires are incapable of bodily functions.

Yes. That's how more and more vampires come into the world. They basically have offspring the same way humans do. It's kinda a different subject I don't wan to get into.

dracula has a son named alucard. (dracula spelled backward) alucard is AWESOME in castlevania!

p.s. no one mention twilight or else!