Can I get in trouble if I submit my own paper as a sole author while employed as a research fellow?
As @Richard Erickson said in a comment, the answer is specific to your university and your contract. Here's the steps I would take if I were in your shoes:
Firstly, read your employment contract. What you're looking for is any language about intellectual property and the results of research. In the comments you mention patents and profits from patents, but that's irrelevant here. If it is specific to patents then it doesn't apply to anything that's not a patent, such as a conference paper. Assuming your contract doesn't unambiguously say that the university owns the IP...
Secondly, go talk to your university legal department. Do not cast this as a dispute. Simply tell them that you were reading your employment contract and wanted clarification about what the university's policy around IP is. Inquire over email, or get them to send you an email confirming their position if you wish to talk in person. If they tell you that their position is that you own the IP to your work, then you're golden. If they tell you that their position is that you don't and you think that your contract doesn't support that claim...
Thirdly, consider hiring a lawyer. This can be expensive and can be a massive waste of time if you're wrong about your contract (lay people generally are, compared to lawyers). Deciding if this is a worthwhile step is a personal decision based on a lot of factors I don't know.
If your university owns the IP, you're likely stuck. Your manager is most likely the person who the university has selected to approve you publishing things, and that seems like a non-starter. If he has a boss who reads your work and is "really in charge" then it might be the boss, but whether you're likely to get anywhere going around your manager depends a lot on the social dynamic.
It's also possible that you can get him to disavow the IP, but I don't really know enough about the details of contracts to comment much on that.
Actually, it sounds like you are well and truly stuck. But only for this one bit of work. If you can risk a lawsuit then maybe not, but it seems like you would have powerful adversaries and little support.
You can publish the work, including all the expected co-authors or simply abandon it as you are leaving. One of the things you will want in leaving, is a decent letter of recommendation unless you have already lined up a new position. It might be necessary to focus on that to the exclusion of other factors to protect your own reputation for the future.
However, since he has discouraged you from submitting to a conference, and you have already given notice of leaving, perhaps you can also give him notice that since he rejected it, you intend to pursue it. You may get pushback or not. But the notice, if properly stated, may free your hand. His refusal to endorse the work might be taken as a release, especially if you submit after employment ends.
In future, however, make sure that you build more realistic expectations into your contract.