What conserved quantity does Supersymmetry imply?

A supercharge is the conserved quantity that corresponds to a supersymmetry. It generates a supersymmetry & commutes with the Hamiltonian.

A supercharge is a Grassmann-odd quantity. Noether's theorem works fine for supermanifolds, cf. e.g. this Phys.SE post.

However, note that one cannot measure (the expectation value of) a Grassmann-odd quantity directly in an experiment, cf. e.g. my Phys.SE answer here. In other words, the experimental consequences of a conserved supercharge are extracted by other indirect means.

The conserved charged is the supercharge, as @Qmechanic told you. But then, what is supercharge? Supposing a particle of momentum $P_\mu$, the simplest SUSY implies a supercharge $Q=ip_\mu\Psi^\mu$, where $p_\mu$ is the momentum and $\Psi_\mu$ is the Grassmann variable, and you can also prove that this thing is secretly a sort of Dirac operator. I have explained some details in my blog, see the appendix of this blog post of mine: http://www.thespectrumofriemannium.com/2015/08/08/log177-scherk-susy-and-sugra/

Moreover, two tips, FOR THE SIMPLEST SUSY: 1) the SUSY transformation of the supercharge is, up to a multiplicative constant, THE SUSY LAGRANGIAN, and 2) the SQUARE of the supercharge is THE SUSY HAMILTONIAN.

In addition to all this, the most general SUSY algebra, as far as I know, can include beyond $P_\mu$ extra topological extensions of the SUSY algebra including central charges. So, in addition to spacetime symmetries, and mixed entities like the supercharge above, you can also get topological charges in non-trivial way. References: https://arxiv.org/abs/hep-th/9711009 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.63.2443