It has been somewhat verified that Jayden isn't the real heir to the Shiba house with the fact that a second, female, red ranger being set to appear, but this could be because Jayden in wounded though. Going by their sentai counterpart, Shinkengers, Jayden will be the vessel of this ranger. Who knows she might even adopt him.
So to answer you question: The chances of Jayden having a sister? slim. Apodtive mother? maybe?