Twin paradox in curved space time

In that case which twin will be older?

Each twin experiences a proper time $\int ds$, where the integral is taken along their world-line. In general, this is all we can really say. However, in the case of a static spacetime, you can define a gravitational potential and then analyze the proper time in terms of two terms, a kinetic term (special-relativistic $\gamma$) and a gravitational one (proportional to the potential).

How to solve the paradox in this context?

The SR paradox occurs if we assume, erroneously, that there is symmetry between the twins. The SR paradox is resolved because the world-lines are different. The symmetry fails because they're distinguishable: only one of them is inertial.

The GR version you've posed is resolved in the same way: the world-lines are distinguishable (although both are inertial), so integrating $\int ds$ along them gives different answers. For instance, one could orbit the earth 47 times in an elliptical orbit, while the other orbits it 10 times in a circular orbit. The orbits intersect at the beginning and end.

First, there is nothing surprising or paradoxical about two geodesic paths from $A$ to $B$ having different lengths. From a point on the equator, you can travel 1/4 of the way around the world to the North Pole while your twin travels 3/4 of the way around the world to the North Pole. Even though you both start and stop at the same places, your odometers show different lengths for your journey.

In the same way, if two travelers take different geodesic paths from one event to another, there's no reason those two paths should have the same length. A clock is a spacetime odometer, so there's no reason their clocks should show the same elapsed time. Which twin is older? The one who followed the longer path through spacetime. Still no paradox.

It's been suggested in the comments that there might be a paradox in the "fact" that Bob's clock always runs slow in Alice's (fixed) reference frame and vice versa. But we're in a curved spacetime, so there are no global reference frames.

So I'm left wondering where the alleged "paradox" is supposed to be.