How does Gohan inherit his "Mystic" power while others do not? Goten and Trunks in the current Z timeline are very powerful, but even the Fused SSJ3 Gotenks can't be compared to Mystic Gohan. He was more powerful than even SSJ3 Goku. 

Even though Gohan didn't train for around 10 years between the Cell and Buu saga, he was able to surpass all Z characters except Vegtito and BuuTenks in power.

So, why is Gohan more powerful then other half-saiyan children?

In this question, the most upvoted (not necessarily correct) answer says that since Goku/Vegeta were more powerful when Trunks/Goten were conceived they were more powerful. Hence why Future Trunks was weaker. But, this doesn't explain why Gohan was the strongest of the lot when Goku was at his weakest in Z when Gohan is born. And, this directly contradicts the answer given above.

This question  may be related, but I believe that Gohan has a hidden power which was released by the Elder Kai answers the question. However, I can't find any source or the reason for the hidden depths to Gohan's power. So, that question may build on the premise of this question.

How does Gohan inherit his "Mystic" power when none of the other half-children such as Future Trunks, Trunks and Goten have it?
Some context before answering the question.


  Gohan vs. Future Gohan (F-Gohan)


F-Gohan was never shown to be nearly as strong as Gohan SSJ2 vs cell, even though he was much older. This seems logical to me as Gohan trained for three years by Goku and Piccolo and then again for a bit less than a year in the hyperbolic chamber by Goku again, who was much stronger than him. F-Gohan never trained before the cyborgs arrived and probably spent his time studying as his mother always wanted him to. Then, after the death of most of the Z-fighters, Gohan trained by himself for years. This I think is the key point: when training with someone much stronger, one's power increases a lot more rapidly.


  Gohan vs Future Trunks


Same reason as stated above. In Dragon Ball super, we see F-Trunks's power increase exponentially and close to reaching SSG, probably just by fighting along side Goku and Vegeta.


  Gohan vs. Trunks and Goten


Trunks and Goten reached SSJ very young. Who's to say they wouldn't become stronger than Mystic Gohan much younger if they followed similar training? They both reached their current level with barely any training, so I'd expect them to become the strongest Z-fighters if they actually trained everyday with their fathers. However, one thing to take into consideration is that they had a nearly-perfect childhood, on the contrary of Gohan. Even when going up against Buu, they had a hard time taking him seriously, maybe never truly grasping the seriousness of the situation.

Answer:

I think there are three major deciding factors for the power of a hybrid human/sayian:


How strong the father is when he conceives the child.
How much pain he has gone through up to a certain point. This may have more effect the younger one experiences that pain
Training, and the power level of whoever you train with.


The potential you've mentioned in the comments is just in my opinion a combination of the above three points. Trunks and Goten lead in point 1 but are truly behind Gohan and F-Trunks in points 2 and 3. Compared to Gohan, F-Gohan certainly leads in point 2 but lacks even more in point 3.

The Great Elder on Namek says he's never seen such dormant potential before but he never encountered a Sayian before, let alone a hybrid human/sayian.

Also, Gohan's power-up against Raditz is not random at all. He sees his father getting beaten up, gets very mad which fuels his power. Raditz then mentioned human/saiyan hybrid may be more affected from rage than regular sayians.