Jordan Stapleton, 21, was found in the bathroom of his home in Beckhill Close, Meanwood, on Tuesday.
West Yorkshire Police said armed officers executed warrants at three addresses - two in Meanwood and one in Scott Hall - this morning.
Teenagers aged 18 and 19 from Meanwood were arrested on suspicion of murder and remain in custody.
Another three people - a 27-year-old man from West Park, a 24-year-old man from Scott Hall and a 22-year-old woman from Meanwood - were arrested yesterday on suspicion of conspiracy to commit murder.
They were released without charge for conspiracy to murder but the 27-year-old continued to be held on suspicion of drug dealing.
Mr Stapleton’s son was asleep in the first floor flat when his father was shot and escaped unharmed.