Although it's rare if taken correctly, you can get pregnant while on an oral contraceptive. If that happens, then you may not realize that you're pregnant right away, meaning that you will, in all likelihood, continue to take your birth control pills until you do realize you're pregnant. This can lead a frantic Google search to find out whether or not your baby will die if you took birth control in the first trimester.
According to the Mayo Clinic, it's not uncommon for women to continue to take their birth control pills in the first trimester before realizing they are pregnant. Although it sounds like something that's potentially terrible, there's not a lot of solid evidence that taking those birth control pills will negatively affect your health or the health of your baby. Women are often concerned that the hormones in these pills will cause birth defects, but, according to the aforementioned article from Mayo Clinic, there's not much evidence of that happening. Of course, once you know for sure that you are in fact pregnant, you should immediately stop taking your birth control pills.
That being said, there are some risks. In a separate article for Mayo Clinic, OB-GYN Dr. Yvonne Butler Tobah wrote that you may have a slightly higher risk of an ectopic pregnancy if you continue to take a progestin-only pill while pregnant. But, again, the risk is quite low.
Other common fears, like the risk of low birth weight, preterm birth, or urinary tract defects haven't been seen much in clinical experience, meaning the risk of them actually happening is extremely low. But despite the odds that your baby will be just fine, Healthline noted that you should see your doctor right away if you're taking birth control and discover you're pregnant. Even if there was no chance for any birth defects, it's also important to seek prenatal care sooner rather than later.
Ultimately, it's unlikely that the hormones from the pills will negatively affect your baby at all. If your main worry is miscarriage, don't fret. In nearly every situation, the little bit of birth control you took early in pregnancy is generally considered safe — for you and for the baby.