Frankly, every household electrical appliance emits some small amount of radiation, but the amount of radiation and the type of radiation that can cause issues with a pregnancy or harm the fetus is different than that which comes from things like computers.
X-rays are the primary source for concern when it comes to a pregnancy. That’s the reason that they always ask if there is a chance you could be pregnant before you have an x-ray and if there is any chance they want to perform a pregnancy test before proceeding with the x-ray. It is also the reason that ultrasound technology is used to get images of the fetus in the womb instead of x-rays. Ultrasounds also emit radiation, but it is a lighter and less risky form for both the pregnant mother and the baby growing in her belly.
There has been some speculation about computer radiation and pregnancy, including the potential loss of amniotic fluid, risks to the baby’s development and concerns regarding loss of the fetus or fertility in general. There is no absolute scientific proof of any of these claims that have floated around on the internet, but if you’re really concerned, I would think there are some things you can do to minimize risk and that don’t involve giving up being on the computer entirely.
Ideally, you should not be resting a laptop on any part of your body anyway, including your pregnant belly. The heat from the laptop is a problem for you and could be a problem for the baby. If a computer is kept at a decent distance from your body, then there should be no problem with you continuing to be on it all the time while pregnant. There are tons of mothers who have done it and had safe pregnancies and healthy babies.