Do I have any rights on the pups if my dog got my neighbor’s dog pregnant?

You would be much better off trying to reach an agreement with your neighbor under these circumstances. You do not say whether or not the female is registered with any accrediting canine registry (e.g. A.K.C.) or if your male dog was, but if so, perhaps they can provide you some assistance, since registries generally require the owners of both to sign documents confirming lineage and the occurrence of the breeding event. Otherwise, you are not generally likely to have any "rights" with respect to the pups.

Not that I am aware of. Perhaps you should offer to buy a pup.