Do i have to amend my taxes which I accidentally claimed my child first, in order for his father to claim him?

Yes, you must amend.

But the father does not need to wait for your amended return to be processed. He can file now and claim the child. He just can't e-file. He has to mail in a paper return.

There's more that he (and you) need to be aware of. There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.

Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the exemption to him.

 So, it's good idea to let the other parent know that you will be claiming those items, as many first time divorced parents are not aware of this rule and may try to claim those items, which will cause the IRS to send out letters.

Ref: https://www.irs.gov/publications/p17#en_US_2017_publink1000170897 Scroll down to "Children of divorced or separated parents (or parents who live apart)"

It is allowed  for you to arrange the children's schedules so that the child spends more than half the year with the father one year and more than half with the mother  the next year so that you are each the custodial parent in the year you claim the child, so that you can claim full benefits.