Normally, there is a scaled version of the Bessel functions J_m(x) and Y_m(x) for large x. Nevertheless, the Y_m functions also diverge quickly for x close to zero, and I would like to ask if there is an analogous scaled version implemented, since I have to deal with this and I am getting overflows
For Bessel functions, you may want to use Bessels.jl which is often faster and more accurate.
I need it to support complex arguments, and judging by the documentation it appears like that package does not cover that.
Not that I know of (in Julia, at least), but for arguments small enough to get overflow you should be able to switch over to the power-series expansion (which should converge to machine precision in just a few terms if the arguments are very small), and thereby implement your own scaled version. From Abramowitz and Stegun, p. 360:
