The spat opens up a subject that has long been a talking point – when did the 40th president begin to become mentally impaired by the disease. He was formally diagnosed with Alzheimer's in 1994, five years after he left office. Reagan died 10 years later at 93.
His sons have written books on the occasion of the 100th anniversary of their father's birth, that falls on 6 February.
The more contentious of the two is My Father at 100, written by Ron, Reagan's natural son with Nancy.
In it, Ron Reagan describes his growing sense of alarm over his father's mental condition, beginning as early as three years into his first term. He recalls the presidential debate with Walter Mondale on 7 October 1984.
"My heart sank as he floundered his way through his responses, fumbling with his notes, uncharacteristically lost for words. He looked tired and bewildered," Ron Reagan writes.
Against that is the word of Michael Reagan, who was adopted by the president and his first wife, Jane Wyman. His book The New Reagan Revolution, is an appeal for a return to his father's political principles of low taxes and small government as a way to making America great again.
He has lashed out at his brother via Twitter. "What a way for Ron to say Happy 100th Birthday Dad," read one tweet.
"Ron, my brother, was an embarrassment to his father when he was alive and today he became an embarrassment to his mother," read another.
The tale of the Reagan brothers is like a miniature depiction of the polarisation that has taken hold in the US in the past few decades. They have come to occupy opposite corners of the political ring. Ron Reagan showed an independent spirit from a young age, declaring himself at 12 to be an atheist when his father was governor of California. He went on to become a broadcaster of liberal and progressive views on outlets that tended to be left of centre, such as MSNBC and the now defunct Air America radio network. Michael Reagan is a conservative activist and much more in his father's mould. He works as a political consultant through the Reagan Group he founded and makes regular appearances on rightwing outlets such as Fox News and NewsMax. He has a talkshow on the conservative network Radio America. Their father's mannerisms while in office – including stumbling over his words, his occasional falling asleep in public, his weak memory – led to much speculation about how early on dementia had set in. The New York Times medical writer Larry Altman even raised the question with Reagan during an interview in 1980 just before he entered the White House. Reagan said he would quit if he developed Alzheimer's while in office. Altman returned to the subject in 1997, after Reagan had completed his second term. Having talked to many of the president's doctors in the White House, he concluded that there was no evidence that Reagan had suffered any of the symptoms of dementia while in office.