If you loose the right over your body then you loose bodily autonomy. If you have to pay a fixed amount of money by law for another person then you no linger have a choice of what you can so with your own body because you have to keep making those payments

https://www.njdivorceonline.com/njpages/childsupport/childsupportenforcement.asp#:~:text=All states also have criminal,for up to 3 years.

All states also have criminal laws on the books to punish parents who refuse to pay their child support.  New Jersey law says a parent is required to support his/her child.  A person who violates the law may be fined up to $100 and/or imprisoned for up to 3 years>

https://www.justice.gov/criminal-ceos/citizens-guide-us-federal-law-child-support-enforcement

For one, an individual is subject to federal prosecution if he or she willfully fails to pay child support that has been ordered by a court for a child who lives in another state, or if the payment is past due for longer than 1 year or exceeds the amount of $5,000.  A violation of this law is a criminal misdemeanor, and convicted offender face fines and up to 6 months in prison (See 18 U.S.C. § 228(a)(1)).

          If, under the same circumstances, the child support payment is overdue for longer than 2 years, or the amount exceeds $10,000, the violation is a criminal felony, and convicted offenders face fines and up to 2 years in prison (See 18 U.S.C.§ 228(a)(3)).

          Lastly, this statute prohibits individuals obligated to pay child support from crossing state lines or fleeing the country with the intent to avoid paying child support that has either been past due for more than 1 year or exceeds $5,000. (See 18 U.S.C. § 228(a)(2)).  Any individual convicted of this crime may face up to 2 years in prison.

So yea you can be locked up for not paying child support even if the child isn't yours