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Is there a source in Hazal specifically for grasping the (front) two ssissith during the recitation of the shema`?

If not, where does it stem from and what is the purpose?

Thanks. Kol tuv.

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I shall excerpt some items from this Beurei Hatefila article that addresses the origin of the custom to kiss the tzizit during Kri'at Shema. Oviously, kissing them involves holding them, so the article addresses specifically your question and more:

Shulchan Aruch Orach Chaim 24:2

It is a Mitzvah to hold one’s Tzitzit in one’s left hand and on top of one’s heart while reciting Kriyat Shema. We find a hint for this practice in the words of the verse: V’Hayu Ha’Divarim H’Ailah etc. Al Livavecha (on your heart). There are those whose practice it is to look at one’s Tzitzit when they recite the words: Oo’Rieetem Oto and to then touch the Tzitzit over one’s eyes. This is a nice custom and a demonstration of a love for Mitzvot. Ramah: Some have the custom to kiss their Tziztit after looking at them. All these practices are demonstrations of a love for Mitzvot.

Also, see Magen Avraham (mentioned in the article) for a somewhat more specific instruction.

Mordechai Succah 563 (excerpt):

If a minor knows how to put on a Talis, his father should buy him a Talis; the purpose is not to fulfill the Mitzvah of Tzitzit but instead it is so that the boy can throw two Kanfot to his back and keep two Kanfot in front of him and hold the Tzitzit in the proper way while reciting Kriyat Shema

Hagahot Maimoniyot on Ramba"m Laws of Tzitzit ch. 3 law 11:

Al Livavecha. On my left hand, I tie my Tephilin and in that hand I hold my Tzitzit while reciting Kriyat Shema. This demonstrates that the Mitzvah is fulfilled by holding the Tzitzit in one’s left hand opposite one’s heart while reciting Kriyat Shema.

But, there is also an opposing viewpoint!

Sefer Ha'Eshkol, laws of prayer, p. 38b:

Rav Notrani held: One who holds his Tzitzit while reciting Kriyat Shema is displaying haughtiness.

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