What is the number of nodes in the molecular orbitals of cyclic H3? A quick google search does reveal the molecular orbitals of this cyclic H3.

However, one source mentions there are are two nodes; while two of my professors said there's one node. Which is correct?

This seems to be a related question - I am not sure. There also is a question on linear H3+ - not cyclic.
In linear $\ce{H_3}$ you have one MO with zero nodes, one with one node and one with two nodes.  When you bend the molecule around to make a cycle, the two nodes in that last orbital merge to make a second orbital with one node.  The two orbitals of cyclic $\ce{H_3}$ with one node are, of course, degenerate when the ring has threefold rotational symmetry.