You really shouldn’t do it, it’s not a good practice. You should always use the jQuery version supplied with WordPress package. If you use your own jQuery version in your own file you would have to update it manually every time the jQuery gets updated in WordPress package.
If you really insist on doing that, the most simple, hackish solution I can think of is to first deregister the original jQuery, then register your file (minified.js) as jQuery. You will surely run into problems of incompatibility with plugins sooner or later.