There is an option for headphone (others are Audio out (fixed) Audio out (variable) and subwoofer.The reason you were not able to control the volume was because you set it to external speaker. For using TV's 3.5mm output, you should not set it to external speaker. I think there should be an option on the TV to select headphone. If not, then leave it at TV speaker. The TV will treat the 3.5mm output as headphone. If this setting is not visible, just try plugging in the 3.5mm cable first, don't switch on the amp, just connect the cable. It might also be the case that it's not a smart TV and will not show headphone plugged in. Don't change any setting on the TV for using 3.5mm output in such a case.
I write this with the caveat that I have not specifically used a Sony TV and I'm just guessing based on my experience with TVs in general.
Will the output voltage of the headphone out be enough for the amp?