Answer: Jamaica has laws for you to establish paternity and collect child support, see http://www.jis.gov.jm/justice/html/20040207t090000-0500_1684_jis_senate_accepts__report__passes__spouse__bill.asp Any court order in Jamaica for this should be honored by the UK.
can I request a paternity test on a child that is grown and I have always said was not mine, does not carry my name, his mother and I never married, I never signed anything
Yes, if the child is not yet 18 you can request that you want at DNA test to establish paternity by contacting the government child uspport agency. If the child is over 18 he/she would have to agree to testing, it can be done by most private labs.