I have a device that doesn't have standard clock. each time its turned on the clock is set to 00:00 but progresses normally (e.g. 90 mins after startup it will be 01:30).
Will ssh have a problem running on this device or it doesn't matter? (time seems important in encryption)
It shouldn't matter - it would certainly not be an issue on a generic Linux-based system, apart from the timestamps in logs etc. not being accurate.
If this particular system doesn't like the lack of current time it may fare better if you use ssh key authentication - if supported - I haven't posted any links and I don't know what would be appropriate for your setup but a Web search will returns lots of info. Out of interest, what's the system?
Edit: Does your system support the NTP time deamon or command? If so you could have it set its clock to the correct time at startup.