The bank said profits before tax not including those settlements dropped 10% to £1.43bn for the July-to-September period.
The result comes a day after the bank confirmed Jes Staley would be joining as its new chief executive.
Barclays said it had seen slow progress with its so-called non-core businesses, which it is selling.
Losses for the package of businesses, which includes some investment bank assets and parts of the European retail banking operation, more than doubled to £337m.
Barclays provided £270m to settle claims in the US over mortgage bonds and £290m to compensate clients over bad foreign exchange rates.
For the businesses the bank plans to keep, including its UK High Street bank and Barclaycard, profit rose 1% to £1.76bn.
Including the £560m hit, and other costs and gains the bank considers to be one-offs, third-quarter profit before tax fell to £861m from £1.22bn a year ago.
Revenues dipped to £6.1bn from £6.4bn for the June-to-September period.
On Wednesday, Barclays announced that Mr Staley will be joining the bank as its new chief in December.
Mr Staley currently works for US hedge fund Blue Mountain Capital Management, and previously has worked for JP Morgan.
Barclays' previous chief executive, Antony Jenkins, was fired in July after falling out with board members.
Mr Staley will be paid £1.2m in salary, £396,000 in pension contributions and as much as £5.5m a year in bonuses, which will mostly be paid in shares. He will also receive £1.15m in shares per year that he will have to keep for five years before cashing in. That is a total of £8.2m for the year, if he is awarded the maximum bonus.
He will also receive shares in Barclays worth about £1.93m to replace shares in JPMorgan he will lose for leaving his former employer.
In a letter to staff on Wednesday, Mr Staley indicated he would focus on areas of investment banking that did not require as much capital - the buffer of reserves it keeps to protect it from unexpected losses. Analysts said this could include such areas as merger advice and trading in stocks.

A report by the organisation suggests men, women and children are being abused "to eliminate public protest".
Many are subjected to virginity tests, rape and gang rape after arrest.
Egypt's Interior Ministry said it would not comment until it had studied the report.
The study notes a surge in sexual violence after the Egyptian military takeover in July 2013.
The perpetrators are rarely held to account and the impunity points to a "cynical political strategy aimed at silencing all opposition".
Police, intelligence officers and members of the military are guilty of targeting male and female detainees, according to the report.
Among the victims are student demonstrators, human rights activists, gay people and children.
Student's ordeal
I saw an officer who was grabbing a young woman by the breasts and I said to him: "If you want to arrest her, then arrest her, but you have no right to touch her breasts."
He grabbed me exactly as he had her, before calling two other police officers to come and hold me. They beat me, insulted me.
In the van they insulted me and beat me so much that I could no longer stand up. Two soldiers started to sexually assault me.
The officer from the start got into the van and said to me: "Come here I'm going to show you if I'm a man." He sexually assaulted me, the soldiers laughed, and then he raped me completely. I was paralysed, I started to vomit blood.
My life is ruined. I'm afraid of my son, my husband and even my father.
The authors said they did not have evidence that commanders were giving the orders, but the scale of the violence - and the impunity - suggested there was a political strategy.
They claim that victims who file complaints are systematically obstructed by the justice system, and face threats and reprisals by police officers and prison guards.
Sexual violence has long been a problem within the general population in Egypt, with assaults dramatically increasing in the years since Hosni Mubarak was removed from power.
Last year, President Abdul Fattah al-Sisi ordered police to launch a crackdown amid growing public anger.
He said sexual assaults, were "an unacceptable form of conduct" and called for citizens to "reinstate moral values in society".
Barclays has reported a fall in third-quarter profits and set aside £560m for more customer refunds and litigation.
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Egyptian security forces are using sexual violence against detainees on a massive scale, according to the International Federation for Human Rights.