Your child's father can file a petition asking the court to do all kinds of crazy things, and the court can say no. This often happens when people write their own pleadings without counsel. If he has no court-ordered parenting time schedule, you cannot possibly be held in contempt of court for not following it. However, be careful! If he has established paternity, there may be a court order that simply refers to the Indiana Parenting Time Guidelines or orders you to agree on reasonable visitation times.
It is possible that the court will simply treat this like a petition to establish a visitation schedule. If you believe there is a good reason to deviate from the parenting time guidelines, you should be prepared to explain why. For infants visitation is typically frequent very short periods of time during the day, but unless there's a very good reason he will be allowed to spend that time alone with his son.
A few hours of parenting time for Dad during the day now and then might be a good thing. I didn't know how to change a diaper or make a bottle when I had my daughter. He'll figure it out pretty fast.
You cannot be held in contempt of court for denial of visitation if there is no order awarding the father visitation.
The answers provided are for informational purposes only and shall not be considered legal advice on your specific fact situation. If you would like information specific to your particular fact situation, please feel free to contact me directly.