The dig organised by the Northern Ireland Environment Agency (NIEA), Derry City Council; Museum and Heritage Service and the Centre for Archaeological Fieldwork (CAF), Queen's University Belfast, is uncovering evidence of Derry's development from the post-medieval period and possibly earlier.
The work is being undertaken at Bishop Street car park adjacent to the City Walls and St Augustine's Church.
On Monday the team of volunteers found articulated skeletons of two adults and a child as well as part of clay pipe stem which the CAF said indicated the finds were from a post-medieval era.
Nails surrounding the child's remains also indicate a coffin which would have decayed over more than 300 years since the burial.
In a blog documenting the progress of the dig, a spokesperson for the CAF said it is likely that more skeletons could be found as the week progresses.
The archaeological experts explained the remains were orientated east-west mirroring the orientation of St Augustine's church as in tradition with Christian burials.
It is thought the project might even resolve a dispute over where the city's founder, St Colmcille, built his first monastery over 1500 years ago.
Archaeologist Emily Murray told UTV: "We know that this was a very important medieval site but we haven't found anything from it as yet. That's why this is so significant, it's allowing us to excavate below plantation levels of the city and hopefully find some of that earlier history."
In the 12th Century a High King of Ireland did die in Derry and was buried somewhere in Derry, we don't know where.
Environment Minister Mark H Durkan said the finds will "hopefully shed a light on what existed at this important site many centuries ago".
"Archaeological excavations are an important way of shaping our understanding of the past and give a valuable insight into our fascinating history for locals and tourists alike," he commented.
"I look forward to hearing of the history of this find in addition to other hidden gems which will be uncovered in the remaining weeks of the dig."
The dig team haven't dismissed the possibility of finding an important figure in history, like the one of King Richard III in a car park in Leicester.
Mark Lusby, City Walls Herigate Coordinator is one of a number of campaigners who wants to see the site preserved when the dig is over.
"Is it appropriate that the foundation point for the plantation centre of Londonderry and the monastic settlement of Derry is sealed under tarmac for car parking?
"Surely this should be a place for reflection or a garden."