Any birth control with a hormone in it can drop your milk supply. Hormones in birth control pills prevent pregnancy by:

• Stopping or reducing ovulation (the release of an egg from an ovary).
• Thickening cervical mucus to keep sperm from entering the uterus.
• Thinning the lining of the uterus so that a fertilized egg is less likely to attach. 

The Pill (estrogen and progestin) tricks your body to think is pregnant so it won’t ovulate. Estrogen based pills will drastically drop milk supply, just like pregnancy does, and should be avoided while breastfeeding unless your weaning. Hormonal IUDs (Mirena, etc), arm implants (Nexplanon, etc), and the mini pill (progestin only) are often recommended as the best form of BC while breastfeeding because most research says that they don’t impact milk supply. Many who use these methods don’t experience any supply drop. For some, though, any hormone based BC will drop milk supply, some times drastically. Every body is sensitive to different levels of hormones. If you have an IUD or arm implant placed and notice a drop in supply, the only way to increase supply again is to remove them. Increased pumping or herbal supplements will usually not be enough to increase supply again because you’re working against hormones. If you’re considering a hormonal based IUD and aren’t sure if your supply will drop, consider taking a few rounds of the mini pill (progestin only) which is the same hormone in the IUD and implant. If your supply drops, you only have to stop taking the pill and your supply will rebound much quicker.