Which Indian state is the origin of the Ajrakh saree?

Gujarat. More specifically, the Kutch district of Gujarat.

The artisan families who practice traditional Ajrakh printing are concentrated in Ajrakhpur village, which was built after the 2001 Gujarat earthquake destroyed much of Dhamadka, the previous centre. Some Ajrakh printing also happens in Barmer, Rajasthan, but the Kutchi tradition is the older and more documented lineage. The Khatri community in Kutch has been printing Ajrakh for generations, with some families tracing their craft lineage back 8 to 10 generations.

If someone is selling "Ajrakh from Jaipur" or "Ajrakh from Lucknow," they are almost certainly selling screen-printed reproductions using Ajrakh-inspired motifs. The printing technique is location-specific because it depends on the alkalinity of local water, the quality of locally sourced materials (camel dung ash, specific iron-rich well water), and generational craft knowledge that does not transfer easily.