I have bad news for you. If the stairs are exposed to weather, I expect this is the case being it is a deck stair, especially freezing temps, then no amount of filler or glue will help. What is causing the split is water is getting into the wood and either freezing, expanding and splitting the wood, or, getting into the wood through a gap in the wood , maybe where there is a loose nail, and rotting.
You could glue and nail as has been suggested , but if I were to do that, I would sister another piece of wood along side of it using pressure treated lumber, as well as putting several coats of paint on the mating surfaces. But the best repair is to replace it with stringers made from pressure treated wood , cedar, or some sort of weather resistant stuff such as trex