I've given gte4289 the point because yes, it is based on a Fiat 1100.
I'm not sure it's actually meant to be a replica but more a loose evocation on the style of the TR250, so your description is pretty near!
It's actually described as a 'Fiat 1100 Sport Barchetta Evocation 1959' but I've had difficulty copying any the pictures apart from the ones below. It's said to have been built in the early 1960s with the body designed to look like a Ferrari Testarossa, but pictures are few and far between and I find it hard to believe it's been around for over 50 years, looking at its condition.
It was advertised on ebay USA for $87,500.