Let us come on words related with Jat. We know that every clan has contributed to society in some way or other. So we will find its imprints in some names. Jat being such a big race will certainly leave impressions on society in some form. We do not find the Jat word in the dictionary I am consulting right now. Though we have other all communities like Rajput, Brahman, Chamar, Kumhar but not the Jat. Then we can not suppose to find directly a word Jat in any Inscription.
So we have to find words related with Jat. Here is list which contain Jata (जट):
जटना - to rob, to snatch
जटल - prattling,gossiping, quibbling, tattling
जटा - tress, matted hair, fibrous root, Spikenard, root of a tree, branch, a method of repeating Vedic mantras
जटाजूट - matted and braided hair of head
जटाधर - an epithet of Shiva
जटाधारी - wearing matted hair
जटाना - to be deceived or cheated
जटामासी - Indian spikenard
जटाल - having matted locks of hair on the head, banyan tree
जटाव - potter's clay
जटित - clotted
जटिल - with matted hair, intricate
जठर - stomach
जाठ - wooden axis of oil or sugar mill, the post placed in the centre of a tank
जुट - pair, batch
जुटना - to unite
जुटली - with matted hair
जुटाना - to gather, to add
जुटाव - combination
All the words have sense of
Uniting or
Shiva's Locks. In Inscriptions we find glorifying of Shiva's Lock but no other God has opportunity to get his hair glorified. You look the image of Shiva. I do not find his lock of hairs as attractive as in Inscriptions. What is the reason? Shiva's Image has
Sun, Moon, Snake on his head or neck. I think this indicates that Shiva United all people:
Suryavanshi, Chandravansi and Nagavanshi to form Jats. Shiva's lock became Symbol of Jats. That is why there is mythological theory of Origin of Jats from Shiva's Locks. So in any Inscription if Shiva's Lock is glorified we should suspect a Jat component there.
Ex.1.
Allahabad pillar inscription of Samudragupta
Samudragupta's fame has been compared with the pale yellow water of the river Ganga, which travelling by many paths, purifies the three worlds, flowing quickly on being liberated from confinement in the thickets of the
matted hair (जटा) of (the) god Pashuupati.
प्रदान-भुज-विक्क्रम-प्रशम-शास्त्रवाक्योदयैरुपर्य्युपरि-सञ्चयोच्छ्रित-मनेक-मागर्गं यश: । पुनाति भुवन-त्रयं पशुपते
र्ज्जटान्तर्गुह-निरोध-परोमोक्ष-शीघ्रमिव पाण्डु गाङ्ग (पय

।।
Ex.2.
Mandasor Pillar Inscription of Yashodharman 532 AD
In the Mandasor inscription of Yasodharman and Vishnuvardhana it is stated that when the river Ganga was about to descend from heaven to earth, in order to break the force of its fall, god Siva (Pashupati) received it in the
matted hair (जट) coiled above his forehead and projecting like a horn; its waters wandered there for a thousand years, before they eventually reached the earth.
Below is the exact English translation of Line containing this:
(L.6.) He by whom (his) head has never been brought into the humility of obeisance to any other save (the god)
Sthanu; he, through the embraces of whose arms (Himalaya) the mountain of snow carries no longer the pride of the title of being a place that is difficult of access; he to whose two feet respect was paid, with complimentary presents of the flowers from the
lock of hair on the top of (his) head, by even that (famous) king Mihirakula, whose forehead was pained through being bent low down by the strength of (his) arm in (the act of compelling) obeisance:
Note - It is to be noted that both
Samudragupta and
Yasodharman are considered to be Jats.