Community leaders say the behaviour needs to be stamped out.
The family’s shed in Murray St went up in flames on Monday night in a blaze fire investigators believe was deliberately lit.
Police yesterday released a still from CCTV footage of a man seen entering the property before the fire.
The family, who moved to Mosgiel as refugees from Syria, say the incident fits a wider pattern of persecution that has left them terrified.
"They chopped the security camera down and the next day they tried to set the fence on fire," a male family member, who asked not to be named, said through a translator yesterday.
"Luckily, it did not work because of the wind."But they weren’t satisfied, so they came back and set the shed on fire."
Emergency services responded to the fire at the Kāinga Ora property on Monday at 7.12pm.
The shed, which was filled with gas bottles and sits near the family’s living room, was engulfed in fire, flames reaching almost to the roof of the house.
The man said this latest incident was another in a series of incidents of harassment and racism the family had faced over the past two and a-half years.
"When my kids go to Memorial Park, people come and verbally abuse them.
"My kids used to go to the park, but not any more — we keep them home."
The children had eggs thrown at them, and verbal abuse hurled their way by other neighbourhood children.
Rocks had been thrown at the family’s car, and through house windows.
The house had also been burgled, he said.
His wife reached for her phone and when she did, one of the men grabbed it from her hands and threw it on to the road.
The family had bought a security camera system with sensors that beeped every time there was movement outside.
Family friend and former neighbour Natalie Sinclair has now set up a Givealittle page to support the family, and raise funds to buy a new security camera system.
When she visited the family at night she would see them sitting in the dark zooming into the camera’s display.
"Every time it beeps everyone’s turning their heads to look at it," she said.
"Nobody should have to do that."
Neighbours would throw a community event for the street to show the family they were supported, Ms Sinclair said.
"We will be doing a circle of protection, having a karakia, some food and a day of games and fun to shake that horrible feeling," Ms Sinclair said.
"But because we [Syrians] can have difficulty speaking up, people doing these kinds of things think we are easier to target."
Mosgiel Taieri Community Board chairman Andrew Simms said many residents and other board members were horrified by what the family was facing.
"We as a community have to stamp [this behaviour] out," Mr Simms said.
Dunedin Mayor Jules Radich said he was saddened to hear of the "completely unacceptable" conduct.
"It simply won’t be tolerated," he said.
Dunedin City Council community development team leader Mai Tamimi said the council would be looking into the whole picture.
"We will go to relevant agencies and discuss what else can be done for the sake of ensuring safety of the family."
Police would not comment on the allegations of harassment and racism, but said they were working with Fire and Emergency New Zealand to investigate the shed fire.
Police had released an image of a man at the family’s home early last Sunday morning.
■Police 105, Crime Stoppers 0800 555 111.