How much should it cost to amend an agreement and to flie them with the court.

Your question seems to involve both child support and child custody.  You can apply to the Department of Social Services to recalculate the appropriate amount of child support based on what you perceive to be a change in the income status of both parties.  You and the mother will be required to provide certain documents to prove your respective incomes and the amount paid for the child's health insurance and any other items that may be a factor to consider, such as private school or medical expenses for the child in excess of $100 per month.  You may not need an attorney if both of you are employees and receive W2 or 1099 wages.  If one of you owns a business, it may be advisable to have an attorney to represent you. With regard to the change in living arrangements, if the mother is in agreement to the change in living arrangements you may be able to draft a simple agreement, but it is often a good idea to at least have an attorney review the draft agreement to make sure that you have the appropriate language and to point out any issues that might need to be addressed for the court to approve the agreement.  If the mother is not in agreement, you will need to hire an attorney to assist you to prove that the change in living arrangements is in the best interest of the minor child.  Another option that you might consider is to see if the mother will agree to participate in mediation to try to work out the details of a change in the custody arrangement. The cost of filing to recalculate child support is very minimal.  Hiring an attorney to represent you in the child support and/or custody matter will depend on your location and the complexity of the case.