It is originally يَتَـشَـقَّـقُ

It is originally يَتَـشَـقَّـقُ (yatashaqqaqu) from the fifth conjugation.

Then the ta lost its fatHah, so the word became يَتْـشَـقَّـقُ (yatshaqqaqu).

Then the ta was assimilated to sh, so the word became يَـشَّـقَّـقُ (yashshaqqaqu).

These are the various steps:

yatashaqqaqu >>> yatshaqqaqu >>> yashhsaqqaqu

There are other examples of this type of assimilation in the Qur'an.

Here is another example:

yatathaaqalu of the sixth conjugation.

yatathaaqalu >>> yatthaaqalu >>> yaththaaqalu.