If I resign from a company which sponsored my US H1B Visa [3 months non-negotiable notice] without another job or company to transfer the visa to, can the sponsoring company do anything which can result in my visa getting canceled?

Disclaimer: I am not a lawyerIf you have not moved to the USA, it may be trickier to transfer. But if you were already in the USA, the risk of not finding a job would be higher, as you would become out of status right away and would have to leave the USA immediately.They can withdraw the petition, but if you passed the lottery this year, you may have the option to transfer cap-exempt for the upcoming 6 years.My recommendation is to get the visa stamp first, if possible, and only then quit. At the very least you should get your application number.On any case, particularly if you quit soon, you should not apply for a company assuming you can transfer the H1B, particularly not before October. After that, you may mention a prospective employer that their lawyer should check if you are qualified to transfer, ideally with the application number and/or visa stamp.

first thing, be cool and you are all good 1. Once h-1b is awarded to a person, its your own award from uscis to work in USA based on your education, experience and specialized skills & nothing to do with company and its liabilities, so your h-1b is not any companies property2. A company which sponsored for your visa can maximum do is stop the sponsorship, meaning your h-1b petition is still yours but you don't have a sponsor to utilize the h-1b (means no job provider for your h-1b at this time)3. if you get a sponsor/company/consultancy who can take over the h-1b sponsorship to your h-1b then you are all good to work in usa to utilize the awarded h-1b, USCIS intention to award the visa is to utilize to max, hence your h-1b is valid to use for max of 6yrs at any number of intervals with n number of sponsors any new sponsor requires minimum of receipt number to take over the h-1b sponsorship to their name, so you need to have minimum of receipt number to which you have all legal rights to know and hard copy of petition should be with you not company once approved per USCIS lawhope this gives you free of mind, you can find a sponsor even after 10yrs not a issue, its expiry is once used for 6yrs, you can be sponsored in India itself, from USA company being in India, you can come to USA on visitor/dependent visa and can find a sponsor who can apply for transfer of sponsorship and apply for change of status you can find lot of ways to utilize the h-1b keeping USCIS rule in mind

So, just having an I797 is not enough. The actual stamping would be required for to be able to be counted against the H1B cap.  Could you please confirm.