Consult with an immigration attorney to determine the requirements.

Gather documentation of your relationship and children's birth certificates.

Ensure that you're complying with all K-1 visa requirements

Be prepared to provide evidence of your relationship and ability to support your fiancé(e) and children.

Yes, you can sponsor your fiancé(e) for a K-1 visa, and your children can be included as K-2 visa beneficiaries if they are under 21 and unmarried.