A scholarship to help you study is fully exempt
The good news first. A scholarship granted to meet the cost of education is exempt from income tax under Section 10(16). There is no monetary ceiling, and the source does not matter, government, a university, an institute, an employer or a private trust all qualify. The only test is that the purpose is to meet the cost of education, which is read broadly to include tuition, fees, and the incidental costs of study. Your residency does not change this, so an NRI receiving an Indian scholarship for education is exempt just as a resident student would be.
A question people worry about is what happens if the scholarship is generous and they save some of it. The courts have settled this in the recipient's favour. In CIT v. V.K. Balachandran [1984] 147 ITR 4 (Mad), the court held that whether the grant is adequate, inadequate or even in excess of the actual need is beside the point, it is enough that the whole object is to meet the cost of education, so a scholar who saves part of it still gets the full exemption. A genuine research fellowship, given to let you pursue study or research, is treated the same way, as an exempt scholarship.
The line: a stipend paid for work is taxable
The exemption is about helping you learn, not paying you to work, and that is where the sharp line falls. If what you receive is really consideration for services, a paid internship, a hospital residency, an apprenticeship or a job where you are paid to do work, it is taxable as salary, not an exempt scholarship, however it is labelled. The courts have drawn exactly this line. In Dr. V. Mahadev v. CIT, an internship stipend that was paid as wages, with tax deducted, was held to be taxable pay, the court noting that such payments do not cease to be salary and become metamorphosed into a scholarship simply because of the name.
So the practical test is purpose, not the word used. Paid to learn, with no work extracted in return, points to an exempt scholarship or fellowship. Paid to work, with the money being the reward for services, points to taxable salary. When it is the taxable kind and the payer is in India, tax is withheld at source, under the salary withholding rules for an employment stipend, or under Section 195 where it is paid to a non-resident as non-salary income. A practising CA looks past the label, fixes whether your grant is exempt or taxable, and sorts the withholding and any refund.