how do i remove bad backlinks from my website?

I wouldnt immediately assume they are punishing you for anything. There can be many other things that are impacting your website fluctuating in rank. The only way to know for sure that google is punishing you for bad backlinks is to check Google search console. If you have a suspicous backlink profile here, they will report it to you. They tend not to tell you the links, but you will more than likely know what they are already. To remove them, you need to use the disvow tool. This tool will allow you to upload a list of bad URLs that you do not want google to attribute to your website. They will then stop giving you a negative punishment for these links and your rankings should go back to normal. The penalty from Google will also be solved by this but it may add your website to a list of spammy sites. You should be always be careful where you buy backlinks from.