How can I find for child abandonment of another parent in Wyoming and how long does it take and where can I file

What is the situaton that your trying to call abandonment ?

If the child was left in the care of the other parent (YOU) then you have no grounds. Is this the case?

You generally don't "file for abandonment". This sticky note (at the top of this forum): https://www.askmehelpdesk.com/family-law/child-abandonment-read-first-364259.html explins the issues in detail.

So you need to explain what you want to accomplish here (custody, termination of rights or what?) Then we can try to help.