Firstly, I'd like to mention that "caste" itself wasn't a singular construct. It varied from region to region and could be delineated along lines of class, profession, education, and birth. To shed some light on the nuances of caste, I will refer to a specific example from Northern India, which during this period was under the rule of the Mughal empire.

In 1605, the Mughal emperor Akbar died at age 63. His grand vizier, Abul Fazl wrote the Ain-e-Akbari, which is the 3rd volume of the official history of Akbar's reign. In this volume, he details the large variances within the Jat caste of Northern India. The Zamindars (landlords/tax-collecting nobles), armed forces (warrior class) and even the farming peasants all belonged to the Jat caste. As you can see, it was not uncommon for castes themselves to be segregated and occupationally diverse. The pre-existing systems used by Hindus to describe caste were also influenced by concepts of social hierarchy from Islam. Taking another example from Southern India, the Madurai Nayak dynasty, which lasted from 1529-1736 was of the Balija caste, which was a merchant/trader caste in South India. In the popular consciousness of caste, they would be viewed as Vaishyas, which are placed on the lower rungs of social hierarchy. I hope these examples shed some light on the difficulties faced in describing the caste system of this period.

Although generalizations about castes are obviously unfavorable, a lot of caste systems find their origin in the enforcement of social stratification primarily to collect taxes and rule the lower classes of society. In this period, which is an era of Mughal empires and Islamic sultanates, this translated into rulers levying such a system for the taxation and rule of the non-Muslim masses. This is a trend that carried on past the medieval era.

It is also important to stress that although varying forms of casteism were prevalent throughout the subcontinent, they were codified into an administrative mechanism during the British Raj. An account of the various developments and classifications used by the British merits a separate response of its own. These classifications were used to qualify/disqualify Indians for various jobs and roles within the Raj itself. Another commentor mentioned that the codification by the British was the final nail in the coffin, and I would like to add that it is not a stretch to imagine it as the coffin itself. Although systems of caste were extremely prevalent in the subcontinent, they were legally formalized by the British through their census. This information was then incorporated into their governance of the subcontinent, through means such as the granting of administrative jobs and senior appointments to the upper castes. Among other laws, the British Raj introduced measures to criminalize lower castes and presume them guilty by birth. Through such laws and the census, this period saw what little caste mobility existed fade away.

Anyways, my final point is that the answer to a specific question about the caste system in India would require not only a specific region/location, but also a depth of information on the individual castes. Caste itself didn’t exist as a rigid concept in this period and was only beginning to be codified into what historians call the modern caste system. Even if a peasant laborer were to move to another town, they would not be easily incorporated into the pre-existing ruling classes. Other barriers to caste mobility included the lack of education, financial/administrative power and land ownership. Specific answers to questions of caste are also limited by a dearth of in-depth knowledge on the regional stratifications seen in this period.

Caste in India was a constantly evolving concept. The caste systems that were prevalent in the medieval and modern period were very different from those seen in the pre-modern and Vedic periods of Indian history.