Is it saying something like "“[App Name] can’t be opened because it is from an unidentified developer” ? If so, you should be able to bypass this by CNTRL clicking and selecting "open" that way.
I usually have to drag the downloaded app into "Applications," then control+click the icon. It'll say it doesn't trust the origin of the file, but there should be an 'open' option anyways. It might take a couple tries to get it to show, but it's always worked for me so long as it's in "Applications" and not "Downloads." I'm sorry if that still doesn't work for you :(