I have two children that are ages 10 and 11. Theie father lives in Texas and my children and I live in Nebraska. He has never even met my youngest and the oldest seen him last when he was approximately 6 months old. I would like to know how I can go about filing about abandonment charges on him to be sure that he can not show up and try to take them from me.

Please read the sticky at the top of this forum on child abandonment HERE (https://www.askmehelpdesk.com/family-law/child-abandonment-read-first-364259.html)

Now that you have done that, you can't file for abandonment. What you can do it file for custody. Until you do, he has the came custody and visitation rights that you do.