Children born from a Spanish man and an Indian woman in the Spanish New World would be considered part of which social class?

People born of a Spanish father and an Indian mother were mestizos.

Explanation:

In the Spanish colonial societies in Latin America, mestizos occupied a middle position in the social ladder. On the top were the peninsulares, or the Spaniards born in Spain, top crown officials, landlords, military commanders; the criollos, born to families of Spanish origin in the colonies, were also members of the economic elite - rich landowners, rich merchants - but didn't have political power; then the mestizos, who were usually free, but not very rich. Mestizos were lower than criollos, but above Indians and blacks who were slaves.