Can i file amended return to claim my son who was not claimed in 2020, and how can he receive his 3rd stimulus ?

My 16yo son lived with my mother inlaw from Jan-April 2020, he moved back to my home end of April 2020 i thought my mother inlaw had claimed him on her 2020 tax return, i found after i had already filed our taxes for 2020 she did not claim him. He also did not receive his 3rd stimulus check. How can i file an amended return and receive credit for him being my dependent and he can receive his 3rd stimulus check. My 2020 return was filed as married filing joint with 3 dependents but really i had 4 dependents because he moved back home at the end of April 2020.
Will this also cause issues with receiving the future child tax credit payments or the adjusted unemployment tax refund?