"I am Ngapuhi, you are not. You don't know what you are talking about," he said, with Mr Osborne countering that Mr Peters, who now lives in Auckland, "abandoned Northland 40 years ago".
"Don't make my record the issue here because you can't defend yours," Mr Peters shot back.
National has been pushing the message that Mr Peters does not have Northland's interests at heart, with ministers calling him "Machiavellian" and "unpredictable".
The byelection winner will replace National MP Mike Sabin, who resigned for personal reasons.
Before Mr Sabin's resignation National could pass any law with just the support of the ACT Party, and a loss would make many laws harder to pass.
The Government has suggested that Resource Management Act reforms and a recent free trade agreement with Korea could be threatened if Mr Peters wins.
Mr Osborne continued that line in the debate today, and said a strong and stable government was at stake if National lost.
"With the numbers in the house at the moment...it means that more partners are needed to get legislation through, and that's at risk."
Mr Peters said National was fear-mongering, and his party was not in Parliament to oppose sensible legislation.
"Kiwibank is a great example, Kiwisaver is a great example - countless pieces of legislation have been passed with our support because someone sensibly came across and said, 'What do you think?'"
