Hi I am a father of 2 year old girl I am not Merridie to her mother but we are living together I am supporting both of them .now the mother want to go . What right do I have as the father I have pay half of lobola

You need to go to court and have a paternity test to prove to the court you are the father.
Then you need to file for joint custody/visitation and child support. It is better you pay child support through the court so there is a legal record of the support. Until you get an order, and even after, KEEP ALL receipts of every dime you send their way whether it is the support order or other money and gifts. Otherwise she can claim you are not providing for your daughter.

Also realize that child support and custody are two separate things and neither one of you can use one against the other.