These are the relationships of the Lighting Ninja Jay.
In Season 6, Jay had learned that he was really adopted and that his favorite movie star Cliff Gordon is his real father which left him very shocked and excited at the thought. After Nadakhan was defeated, all of the wishes have been undone and Jay has not received his inheritance yet.
The previous elemental master of Lightning is Jay is real mother, while Jay has discovered that Cliff Gordon is his real father he does not who his mother is. It is unknown whether she is still alive or why she and Cliff left Jay in the care of the Walker family. It is also unknown whether Jay will find out about her or if he will meet her in future seasons.
Jay's adoptive dad. Jay is very close to his adoptive father and has inherited his habit of inventing things. In Season 6, when Jay made a wish to Nadakhan he received a letter saying his father passed away and he has inherited his fortune. Immediately, Jay rushed to his parent's home where he called out for his father only for Ed to come out alive and well. Jay was relieved at the news but questioned the contents of the letter, Ed and his wife decided it was time to tell Jay the truth and inform him that he was adopted.
Jay's adoptive mom.
Nya is Jay's 'girlfriend'. In the beginning they barely spoke to one another but Jay started to develop feelings for Nya while she did not return his feelings at first. Though they grew closer and starting dating and were happy each other. The two reached a rough patch in season 3 when Nya started developing for Cole and this continued in season 4 where they make up. In Season 5, Jay discovers from a reflection of his "future" that he will get back with Nya inspiring him to pursue her again.
In Season 6, Jay goes through with his attempts using his wishes to try and impress her but in the course of the conflict with Nadakhan, Nya makes it clear to him that they are just friends much to his dismay. However, in the season 6 finale when Nya nearly dies Jay uses his last wish from Nadakhan to undo the recent events done by the Djinn which brings her back to life. Nya and Jay reconcile their relationship and start to date once more.
Jay is one of Master Wu's students along with the other Ninja. When Jay and the others trained to become Ninjas, they showed that they really cared about Wu and glad to have him as their master.
Like the other Ninja, Jay respect Wu who in turn views him as he expressed concern for the latter when he was attacked by Acronix and began to rapidly age due to the affects of the time blade. Along with the ninja, Jay wanted to find his master after he was lost in time with the Time Twins.
They have not interacted a lot in the series but they care deeply about each other and have gotten closer as the series goes on. At first, Kai didn't like the thought of Jay dating his sister due to his overprotective nature but soon came around to the idea.
They are good friends until season 3 when Nya started developing feelings for Cole which initiated a rivalry between the two which continued in season 4. The two reconcile their friendship during their fight on Chen's Island and Cole even sacrificed himself so that Jay could win the battle.
In Season 6, it is mentioned On a Wish and a Prayer, that in spite of the previous rift between them that Jay considers Cole to be his best friend. In Day of the Departed, when Cole was feared lost after facing Yang, Jay broke down and stated he'd give up anything to have Cole back which the latter overheard before revealing himself. Jay and the others were relieved that Cole was safe and human again.
Like all the other ninja he thought Zane was weird but when finding out that Zane was nindroid, he and the others supported and accepted their friend. They grew close throughout the series, with Jay being distraught by Zane's death after he sacrificed himself to defeat The Overlord.
In season 4, he was looking at his portrait of him in sadness and reflecting on their time together. When Lloyd suggested replacing Zane, Jay heavily protested the decision to do so but was shocked to learn that his friend was still alive and traveled to Chen's Island to find him. While imprisoned by Chen, Jay was reunited with Zane and was elated to see his friend again and complimented his new form.
Lloyd and Jay are good friends. They don't talk much, but as the series go on, they grew closer. In season five, when Lloyd got possessed by Morro, jay and the other ninja will do everything they can to get their friends back. In Season 7, Jay was the first ninja come to the decision to make Lloyd their master after Wu is lost in time with Time Twins.