case reports are easy to write if you have a truly interesting case, and someone always needs a book chapter to be written for them. you should ask your attendings if they need help with anything. these are low hanging fruit. systematic reviews are a reasonable thing to get done as a resident as well. you will need to find a topic no one else has tried to summarize yet. that isn't as easy
you can try to get involved in a prospective RCT if your attending has one going. you will need faculty PI to get through your IRB. how far you get with this in the short fixed time span you likely have will depend on the challenges with funding, IRB, and amount of RAs you have on board. MOST folks I meet don't really care to do these things. they are typically lacking in the skillset for research, time, or patience. If you are trying to do research out of interest then you may find it rewarding. if you are trying to beef up your CV to get a fellowship spot... it may not be necessary. I have met pain fellows that did zero research and obtained positions.