Have you questioned any of this news at this point, or are you simply taking everyone at their word..? FYL; although, if your answer is 'no, and yes'... then YDI.

What in the....? The mother is a jerk for telling the son who the father is but not the father he has a kid. The son is a jerk for putting on expectations to a clueless stranger. Maybe it is his horrible way for the OP to connect with the grandkid so they can have a relationship that the OP and his son never had? Or every other grandparent doesn't want to help with the baby and he is grasping at straws. What a mess.

I would be getting a DNA test to be positive. I would simply decline their offer because they are complete strangers. If they'd like to get to know you that might be great in the end. - just a suggestion The mom might have kept it a secret from your child as well- but it's a very odd request to ask a stranger to watch their child.

This sounds a bit like a set up. Pretend to be someone's child, ask them to take care of your own child, have something happen to the child or fake it, put the blame on the "grandparent," and sue for emotional damages or recompensation for medical bills. Politely inform them that you would like a DNA test to confirm the relationship, but that you aren't able to care for the child regardless of the outcome of said test. If she backs down, see if there's someone you can report a potential scam to- maybe police, since if it is a scam, it is child endangerment. It honestly feels like child endangerment even if it isn't a scam- drop off a child with someone they've never met, have minimal information on, and could be in a murder cult for all they know.

How old are you?