Running and outside antenna and Cable internet

Hi. You can't mix two signals from the air and cable. You connect antenna coax to TV antenna connector.

If it was just mixing signals on different frequencies, you might be able to do it with the appropriate filters. However there is the upstream (cable modem TO cable company) channel to consider. I expect it'd be easier to put in a new cable for the modem, and use the existing ones just for TV.

Hi, Cable carries FM radio, TV channels upto couple hundred channels including HD, Voip phones. You think there is brick type filter which can be used to share the coax? I think not.

And so far, no one has commented that absent some one-way blocking device, you now have an antenna connected to the cable system, radiating it's signal into the air. There are regulations that cover how much leakage cable systems are allowed, cable systems are designed and maintained to minimize any such signal being emitted, etc. Hook up an antenna to you cable line and you'll be a small transmitter.