I have a Kohler 15.5 riding mower and was not getting spark so bought a new coil and adjusted it properly but no spark to the plug is happening. I took off the wire to the coil and tried the spark plug grounded to the engine and did get spark.
So, I don't know what it could be? Any help would be appreciated.

I have no spark unless I take the wire connection to the coil on my 15.5 Kohler engine riding mower. I did replace the coil, the spark plug and battery is charged, so I need help with the other possibilities the problem could be?

If it uses a Coil with points and a capacitor, the coil fires when the points open.
Verify your kill circuit, disconnect at coil for a test. If it grounds the mag for killing, be sure it is not grounded.
Disconnect kill switch. Be careful.