I know and use Clinical Trials.gov but it doesn't often give precise results while searching based on gene or protein name/symbol and that can be quite cumbersome.
is that the "clinical trial" section of NCBI does not give you satisfaction? I think that you find results of finished clinical trial (not currently running) but you can select results by protein or gene targeted.
I think you should try NCBI for this. However, there may not be an exhaustive list of all the project which are still in the continuation but most of the molecules being analysed for their clinical relevance may be found.
Go to google (or NEJM) for FDA approved drugs against a target gene, for example, EGFR, then put the related drug name into clinical trail.org. you will have the details.