Was the bozo that wired those circuits trying to burn your house down?
Assuming that the wires are 10AWG (i.e. 30A), this is a major problem indeed as the wires can overheat badly from excessive current draw before the breaker ever notices something is wrong! Think of what a live toaster element inserted into your wall would do...
As to the Code, your issue violates 210.19(A)(1):
(1) General. Branch-circuit conductors shall have an ampacity not less than the maximum load to be served. Conductors shall be sized to carry not less than the larger of
210.19(A)(1)(a) or (b).
(a) Where a branch circuit supplies continuous loads
or any combination of continuous and noncontinuous loads,
the minimum branch-circuit conductor size shall have an
allowable ampacity not less than the noncontinuous load
plus 125 percent of the continuous load.
(b) The minimum branch-circuit conductor size shall
have an allowable ampacity not less than the maximum
load to be served after the application of any adjustment or
correction factors.
and 240.4 (the exceptions in A-G do not apply to your case):
240.4 Protection of Conductors. Conductors, other than
flexible cords, flexible cables, and fixture wires, shall be
protected against overcurrent in accordance with their ampacities specified in 310.15, unless otherwise permitted or
required in 240.4(A) through (G).
This thing is a shut-off switch, basically.
Many air conditioning units have a shut-off switch near them. This panel is designed to be that, and also provide overcurrent protection, and optionally GFCI. It is a 2-space "panel" which is designed to fit exactly one 2-pole common breaker. (any of the THQL THHQL TXQL or QPF types). It is designed to provide a) a shut-off, b) overcurrent protection, and optionally c) GFCI to a single load. It'd be a great hot-tub shut-off.
GE's slick design with THQP and THQQP breakers uses a clever way to do double-stuff 2-pole breakers. Since it uses half-width breakers, it simply uses a 2-pole breaker that sits in the halfway position, one contact on each bus bar. Any number of 2-pole breakers can be stacked like this, if your panel is wide enough. which yours isn't. As such, the only supported 2-pole configuration with these breakers is the 2-pole THQP sitting in the middle, in the 2-3 position, with a half-width breaker on either side. You cannot handle-tie the two outside 120V breakers because GE is quite specific that these breakers have an internal common trip mechanism. Handle ties only assure common shut-off, not trip, so one side tripping could leave the other side energized - bad!
However GE doesn't seem to make a quadplex 2-pole for it. That makes sense. The whole selling point of THQP is to avoid the duplex/quadplex model entirely.
The bigger problem is your wiring.
This really nags at me: Why would someone run 6 AWG to a shut-off switch to a single 30A load? Makes no sense. An installer would install 10 AWG throughout, unless he was some sort of visionary genius, and if he was, he'd have installed more than a 2-space "panel"! So I deduce the wire back to the panel is probably 10AWG and cannot support a second circuit. You would need to replace it with 6 AWG to support a 23-30A main air conditioner and a 15-20A auxiliary load. In fact, in some conditions 12AWG would be legal here!
Given that you may have to replace all that anyway...
...you might go ahead and replace that tiny panel
Normally changing panels is a bugbear, but you've only got 2 cables coming in/out of it so far. So now's the time.
I recommend people get 2-3x the panel they think they need. In your case since you need 2 240V circuits (4 spaces), I'd say go for a 12 or even 20 space panel. Panel space is cheap, unlike regrets, and panels often come with free breakers!
Best Answer
why not use the 50 amp for sub panel then come off the sub panel and feed the AC with 15 amp. You would then have 35 amps for basement circuits.