My concern is, If 120V fixture (Line - Neutral) is connected to A phase, then I would put the current drawn in the Ia column (current in A phase)
For 208V fixture (Line-Line) connected to B & C Phase, Should I mention the current in both B & C Phase?
I agree with Larry's "Yes." But I disagree with the question. The information you insert into a panel schedule is the power, in units of VA, and not the current, in units of amps. As an example, if you have 10 amps worth of lighting load on a 208 volt, single phase circuit, then you convert the 10 amps to VA by multiplying 10 x 208, to get a total load of 2080 VA. Then you put half of that (1040 VA) on phase B and the other half on phase C.
Charlie's way of using volt-amps is the best way to do it because power is conserved, and so it's less likely to make errors using VA's.
However, if you really want to do it with currents, then to do it correctly you need to add up the equivalent "line" currents on each phase. In Charlie's example the line current on both Phase B and on Phase C from the 208V load would be (sqrt(3)/2) x 10A = 0.866 x 10A = 8.66A. Note that this current develops the same VA as Charlie came up with because 120V x 8.66A = 1040 VA.
The Line-Neutral load currents need no correction to get their contribution to the line current on each phase, and therefore they can be added together directly on each phase.