The progestin only pill or mini pill prevents pregnancy by thickening the mucus inside the cervix which prevents the sperm to travel. It also thins the uterus lining so the the fertilized egg won't get implanted.
The mini pill is prescribed by a health care provider if someone is breast feeding, has a certain health problems or experiences side effects from estrogen.
Sources:
https://my.clevelandclinic.org/health/drugs/17707-minipill
https://www.nhs.uk/conditions/contraception/the-pill-progestogen-only/
https://www.webmd.com/sex/birth-control/mini-pill
https://www.healthline.com/health/birth-control-pills#types"
https://www.mayoclinic.org/tests-procedures/minipill/about/pac-20388306
"https://www.webmd.com/sex/birth-control/birth-control-pills