Normally you try very hard to avoid any cold joints in this region near intersecting beams.  In fact, we usually require the contractor to lay out all his planned construction joints and submit them for approval.  We specify that the joints should cross only areas within the middle third of any span.

If for some reason you cannot achieve this, then a cold joint at an intersection can be dealt with.  You simply have a shear friction situation and your reinforcing, above and beyond what is needed for flexure, must be added across the joint to satisfy the shear friction capacity. The joint should be keyed or otherwise intentionally roughened.

See Chapter 11 in the ACI code under Shear Friction for the method.

But I would avoid the situation if you can.