Question: I need to test my under-development Saas web application continuously for some months without incurring any monthly costs. Is there any free Linux VPS hosting available ( with root access ) for this purpose?
Answer: For your purpose of a free VPS to test something without incurring any cost, you may opt for Amazon EC2 free tier hosting which provide 12 months of free unmanaged hosting. Amazon free tier is perfectly fine for starter websites and applications but setting up and configuring EC2 by yourself might be difficult. You may hire an expert individual or company who can get your AWS EC2 server configured on your behalf and still save hundreds of dollars worth of hosting cost for one full year.
Apart from the above Amazon EC2 option, you can go for any trial VPS hosting and then cancel your plan before you incur any charges. You can also switch to another provider if one trial period expires. This may add some switching or migration effort on your side but will solve your purpose of not incurring any costs
Alternatively, there are some hosting servers that give substantial discounts on hosting for educational purposes or for students to test their apps. So if that is the case with you, you can check for some providers offering student discounts.