I'm not sure about how other regions use "jornada", "tiempo parcial" and the preposition "a", but you won't hear these words used like this in Mexico.
"Jornada" is rather used for the work manual labourers do. And for a part-time, we would most probably say "media jornada".
"Tiempo parcial" is well understood, but we don't use it.
Here, we normally say:
No quiero trabajar tiempo completo.
Soy empleado de tiempo completo.
Quiero trabajar medio tiempo.
Soy empleado de medio tiempo.
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