Police are appealing for witnesses after the incident in Bexhill Road at around 6.20pm on Friday evening (July 10).
The 65-year-old, who had been cycling near the junction with Harley Shute Road, suffered a head injury.
He was taken to the Royal Sussex County Hospital in Brighton, where police say he remains in a serious but stable condition.
Then on Saturday (July 11), police said a 37-year-old man contacted officers to report he had been hit with a pellet from a BB gun – fired by a man in a passing vehicle.
This happened at around 12.30pm on Mount Pleasant Road in Hastings, and did not result in serious injury, police said.
Investigating officers are keen to hear from anyone who witnessed either incident, particularly anyone who may have any relevant dash cam footage from Bexhill Road at the time of the offence.
Anyone with any information is asked to contact police online or by calling 101 quoting Operation Falmouth.
Sussex Police say a 26-year-old man from St Leonards has been arrested on suspicion of causing grievous bodily harm with intent.
He remains in police custody at this time.
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