Scaramucci was on Air Force One on his way to the President's speech at the National Scout Jamboree when Ms Ball had the baby two weeks early, on July 24. He sent his wife "a short, congratulatory text". She filed for divorce after the birth.
In the bitter fallout after they split, former Wall Street executive Scaramucci reportedly ordered a paternity test for the newborn.
I'll WORK WITH TRUMP AGAIN
Since leaving the White House, Scaramucci has launched a media venture called the Scaramucci Post, talked about a book or a movie about the West Wing, and in an interview with the Boston Globe, insisted his ten-day White House tenure was a resounding success.
He told the publication last month he remains in close touch with the White House, although he hadn't spoken with Trump for more than a month.
''I have very good relationships there still, and you have to remember we were a team for 18 months, and so we all had different roles. And so I'm still playing my role frankly. I'm an advocate for the president, media surrogate when I need to be,'' Scaramucci said.
He said he was concentrating on his own businesses, but expects to help out at Trump's re-election campaign.
Of his short tenure, he joked that he had expected his term at the White House to have a longer shelf life than a ''carton of milk.''
And he said it was successful because he helped bring the issue of unauthorised leaks under control.
''We identified quickly who many of the leakers were, and they're gone,'' he said. ''You and I both know the leaks are down substantially. And that's a positive thing for the president.''