Tandoori paste is a classic east Indian marinade. But like any seasoning combination that has been made at home and in restaurants over many decades, everyone has a different recipe. The bottled products that are available in Indian food markets and online are generic products that, like curry powder, probably were evolved by repatriating British colonists who wanted to recreate Indian dishes back home.
You can certainly make tandoori paste at home, but it demands a certain depth in the spice rack. Here is one method:
Toast two tablespoons each of coriander seeds, cumin seeds, and fenugreek seeds, one tablespoon each of black peppercorns and cloves, and a teaspoon of cardamom seeds in a skillet over medium-high heat for about a minute. Remove them from the heat, let them cool and grind them to a powder in a spice or coffee grinder. Mix with 1/4 cup of paprika, a teaspoon of ground fenugreek leaves, 1 tablespoon of ground cinnamon, 2 teaspoons of ground ginger, and a teaspoon (or as much as you can bear) of cayenne pepper. Mix with enough peanut oil to form a thick paste.
Tandoori paste is often mixed with yogurt, minced garlic, chopped onion, lemon juice (and often ginger, as well) to make a specially flavorful marinade.