Peel the potatoes and cut them into 2 cm. pieces. Place the diced potatoes into a pot of cold water, bring to a boil over high heat, and then reduce to a simmer. Cook for 15-20 minutes until fork tender.
Drain the potatoes in a colander or wire mesh strainer, and run cold running water on them for 1-2 minutes to cool them. Allow the potatoes to fully drip dry in the colander before moving to the next step.
Add cornstarch, ajwain seeds, chaat masala, amchur, Kashmiri red chili powder, minced cilantro, minced green chilies, asafetida, and salt to the potatoes.
Mash thoroughly until all the ingredients are evenly distributed.
Divide the potato mixture into 3-tablespoon portions. With clean, slightly moistened hands, press into 1 cm. thick smooth round patties.
Heat the oil in a frying pan or skillet over medium heat. After 2 minutes, when the oil is hot, pan fry the patties in batches for 4 minutes on each side until all patties have been fried. If necessary, add a little more oil to the pan between batches. Let all fried patties drip dry and cool slightly on a wire rack before serving.
In a small bowl, make the dahi by combining unsweetened yogurt, chaat masala, ground cumin, lemon juice, jaggery or your choice of sugar, salt, and water. Mix with a small whisk or tines of a fork until smooth.
To serve, place the potato patties onto a platter (or if serving as individual servings, 2 pieces on each plate). Drizzle with cilantro chutney, tamarind chutney and the yogurt dahi. Garnish with minced red onion (if using), a sprinkle of chaat masala, fine sev, fresh cilantro leaves, and sliced green chilies.