The claim that Obama orchestrated a coup in 2016 is false and not supported by credible evidence.
Trump claims Obama orchestrated a coup in 2016

Trump falsely twisted an Obama-era assessment of Russian election interference as a ‘coup’ - Poynter
Source: poynter.org
Key Evidence
Trump's claim that Obama led a coup is contradicted by official intelligence assessments and bipartisan investigations that found no evidence of such a conspiracy.
Obama publicly denied the allegations, describing them as 'bizarre' and unfounded.
Fact-checkers like PolitiFact and Poynter have labeled the coup claim as false and misleading.
What the Evidence Shows
Former President Donald Trump has publicly accused Barack Obama of orchestrating a 'coup' against him in 2016, alleging that Obama led efforts with Hillary Clinton and others to subvert the 2016 election results. However, multiple fact-checking organizations and credible news sources have found these claims to be baseless. A coup implies an attempt to prevent a duly elected president from taking office, which did not occur.
The intelligence assessments during the Obama administration regarding Russian interference in the 2016 election were based on investigations and evidence, not a political conspiracy to overturn the election. Obama and his representatives have strongly denied these allegations, calling them 'bizarre' and a distraction. Independent reviews, including those by intelligence officials and bipartisan Senate reports, have not substantiated any claims of a coup or treasonous conspiracy by Obama or his administration.
These accusations are widely regarded as politically motivated and misleading.