Rosdeep Kular, 33, posted a picture of herself with Mohammed Abdi the day after he died in the Willowbrae area of Edinburgh last April.
Neighbours say they had seen Mr Abdi, who was 25 when he died, coming and going from Ms Kular's flat and that he had been a regular visitor to her home in the Drylaw area of the capital.
One neighbour, who asked not to be named, said: "It has been a long time since I last saw him, but I have definitely seen him with the mum.
"I don't know if he was her boyfriend or anything, because there was always a lot of people coming and going, but I have definitely seen him over there."
Another said: "I saw him a couple of times but more with the kids than with the mum. I'm sure that he took the little ones to nursery too."
Mr Abdi, whose father was an Imam at the Edinburgh Central Mosque, died on April 26 last year.
Six men deny killing Mr Abdi. Mohamud Mohamud, 30, Ahmed Ahmed, 28, Cadil Huseen, 22, Hussein Ali, 26, Liban Ahmed, 29, and Said Fadal, 32, appeared at the High Court in Glasgow over the alleged shooting earlier this month.
Mr Abdi was allegedly shot with a sub-machine pistol and a revolver.
Ms Kular, who has four other children, works as a beauty therapist.
Her family originate from India.
She has sons Tarun, nine, David, seven, and daughter Renuka, five, with her Nigerian ex-husband Omotoso Adekunle Adekoya, 35, who she married in Glenrothes, Fife, in 2004.
But she split up from her husband, a taxi driver, and found a new boyfriend.
She later gave birth to Mikaeel and twin sister Ashika in 2010.
A former neighbour of Ms Kular, Patricia Kilpatrick, 72, is reported to have said: "She wasn't with her husband anymore.
"I remember there being a problem one day with her husband who had come to take the kids on a Sunday but he couldn't get them from inside the house.
"He used to come and take them away for the day, I think to his house, but not all of them, just his kids.
"He had come on the Sunday to pick them up but I think he realised that they were alone in the house and soon after that the police arrived to sort everything out.
"He was a taxi driver and he would always arrive in a taxi and take them away in it."
Mr Adekoya lives at a flat in Waterfront Gait in Edinburgh, just five minutes' walk from Ms Kular and her children.
Just before midday on Thursday, 20 police officers raided a property in his street and made an arrest but officers later said that the raid was an unrelated operation.
Mikaeel's grandmother, retired doctor Harjinder Kular, joined the rest of the family in Edinburgh as the search continued.
Harjinder's neighbour April Mullen met Mikaeel and his siblings many times when they came to her garden to see her fish pond.
She said he was "quiet and sweet-natured, just like his brothers and sisters".