To "compel" anyone to do anything will usually require a valid judgment. Without information about your marital status and detailed answers about you, the mother in question, the child, and your relationship, it would be really difficult to say what would happen in a lawsuit.
Talk to a lawyer from your state about visitation rights. If you are divorced, then this should have been detailed in a judgment or separation agreement. You are entitled to have access to your child... unless you happen to be a really terrible person (in that case, the judge would probably not give you what you want).
I am assuming from the info that you have provided that you and the child's mother were never married. Assuming that it true, you need to establish paternity as soon as possible. You should know that establishing paternity will also likely establish a child support order as well.
This answer is not intended to create an attorney-client relationship between the reader and Matthew R. Shipman. The information is intended for general informational purposes only and should be used only as a starting point for addressing your legal issues. It is not a substitute for an in-person or telephone consultation with Mr. Shipman to discuss your specific legal issue.
Matthew R. Shipman
Bloom Gates Sigler & Whiteleather, LLP
119 S. Main Street
Columbia City, IN 46725
Telephone: (260) 248-8900
Fax: (260) 244-3913