Parental Authority of my child

Good Day to you, I want to ask for your opinion. I have a 1yr old son and the father and i aren't not married. I'm going abroad in a couple of days. at first, my parents and i had an agreement that they(them and my baby's father) will share custody of the child meaning that my child will stay for a couple of days with his father and another with his grandparents but now they are telling me that the father cannot take the baby, he can only come and visit the child in their house.
i'm asking if they can invoke parental authority on my child while i'm away? because i want for them is to share custody of my child. what legal actions should i take?

only the mother of an illegitimate child has parental authority. but it cannot be exercised by proxy. but if a case is filed, i would side with you to win as long as you signify you are not abandoning your child.

why did your grandparents deny the child from going with the father? is there a threat that the child will not be returned?

they think that they can do a better job of taking care of my child, i already explained to them that i would be more comfortable that my child should also have time with his father. I told them that the father is willing for a shared custody so that my son can also spend time with his grandparents, the father already agreed to have the only for 3 days and the rest of the week his with my parents.. Now my parents are demanding that the father should have a job first before they agree to let him borrow the child. I'm so frustrated because it is as if i don't have the right to decide what i think is right for my child. They keep telling me they are my parents and they know best i'm only afraid that they will cut me off especially they are the ones who will be financing my studies abroad.

keep talking to them. arrange for some limited visitation by the father. it can be supervised by the grandparents, if need be. while it is not a legal requirement, it may go a long way that he does get a job.

you must be willing to give up their support if you will be going against them and assert your rights.