Chandragupta Maurya took the Punjab from Alexander's successors and Ashoka governed Taxila as a prince before he became emperor.
Ashoka's rock edicts at Shahbazgarhi in Mardan and Mansehra in Hazara are the north-western edge of the series. They are in Prakrit written in Kharoshthi, the script of the north-west, which runs right to left and derives from Aramaic.
The Kandahar edicts, further west, are in Greek and Aramaic. The Mauryan administration wrote to its subjects in the language and script each region used.
Kharoshthi was the writing of Punjab and the frontier for centuries and then died out completely, replaced by Brahmi-derived scripts. Gurmukhi descends from the Brahmi line, not the Kharoshthi one.
A script used across this region for six hundred years disappeared so thoroughly that it had to be deciphered in the nineteenth century from bilingual coins.
Taxila was a provincial capital and Ashoka governed there as a prince before his accession. Its ruins are near Rawalpindi and are on the world heritage list.
Kharoshthi was written right to left and derived from Aramaic, which had come with the Achaemenid administration. It was used across Gandhara and the Punjab and along the trade routes into Central Asia.
It was deciphered in the nineteenth century using bilingual Indo-Greek coins. Without those coins the script would still be unreadable.