In 1878 a treaty was signed between Maharaja Ranbir Singh's government and the British to establish telegraph lines between Jammu & Srinagar as well as between Srinagar & Gilgit, the first being of primary interest to the Maharaja and the second to the British (as they were concerned about the Northern borders and central asia). Perhaps due to this reason, Jammu & Kashmir was the only princely state that was allowed its own issue of Telegraph stamps.
Patiala can be also considered to have issued telegraph stamps. Stamps of Patiala overprinted 'Telephone' were in reality telegraph stamps. Supposedly the Maharaja of Patiala wanted his own telegraph system like Jammu and Kashmir to the north. The (British) Indian Government said “No!” , so they set up a system whereby messages were dictated and transmitted by word of mouth instead of by morse, called it a telephone system and printed ‘Telephone’ on the stamps to prove it.
Jammu & Kashmir telegraph stamps are especially rare on piece (used on telegraph receipt forms). Dawson, Eames, Kashmir Blue - none of these famous collections had a single such item. The Haverbeck auction had mentioned two such forms. After a census, I have come to the conclusion that less than 10 such pieces (optimistic!) exist in collections. There were two types of telegraph receipt forms used - the standard British Indian Telegram receipt and a native receipt (totally different in design and with writing in persian). Of the latter perhaps just a couple exist (including one in my collection).
Another part telegraph form with three "TWO/ANNAS" (serif) on 2r dark brown and blue and "8 ANNAS" on 5r green and red.
Frits Staal , The Stamps of Jammu & Kashmir
Hiscocks Document on Patiala