The custody is with the mother as long as she does not remarry.
Kindly refer to the following link(s):
https://www.youtube.com/watch?v=U5GK8Wk9LFE&app=desktop

On behalf of a sister – If a Muslim woman is divorced by her husband and has a young baby under the age of 1, can the father take the child from the mother or is the child better to stay with the mother? They live in the UK.

Custody | August 31, 2017 8:43 pm
Previous

If divorced woman has kids and she wants to remarry, will kids be taken with her to her new husband’s house?
Next

QUESTION: Sheikh, what is the ruling and punishment for a man who has the means but does not provide for his wife and for a man who does not provide for his children (full/proper maintenance) in a divorced home.