Consult with an immigration attorney to determine the requirements.

Consider seeking guidance on K-1 visa application process and potential implications for your children.

Absolutely, as a U.S. citizen you can sponsor your fiancé for a K-1 visa even if you have children together, having children together is not a barrier to filing the petition. Your fiancé(e) can also bring eligible children (under age 21 and unmarried) with them by applying for K-2 visas for each child as part of the same process