Did former President of the United States Barack Obama send a tweet about asking Ukraine if they found his birth certificate? No, that's not true: the viral image making that claim is not a real screenshot of a tweet.
While we're at it ask Ukraine if they found my birth certificate
This was the image in question:
No trace of such a tweet is present in Obama's Twitter history at the time of writing. We also checked the Internet Archive for a saved copy of the tweet and didn't find it. Politwoops, a website that automatically keeps track of deleted tweets from politicians, also doesn't have it. Neither does a bot account on Twitter-like service Gab that automatically reposts all tweets from the @BarackObama twitter account. So it doesn't seem likely the tweet once existed but was deleted.
Interestingly enough Obama's last full-text tweet (at the time of writing) is this one from September 20, 2019:
One challenge will define the future for today's young generation more dramatically than any other: Climate change. The millions of young people worldwide who've organized and joined today's #ClimateStrike demand action to protect our planet, and they deserve it.-- Barack Obama (@BarackObama) 20 september 2019
If you check the version saved in the Internet Archive on October 5, 2019 it appears it had the same number of likes and retweets that are shown (rounded) in the screenshot of the false tweet: "40,544 Retweets 248,119 Likes". Note that the mobile version of Twitter's website shows like and retweet counts as rounded numbers, so 40,544 would become 40,5K. Here is the version in the Internet Archive if you want to check for yourself:
One challenge will define the future for today's young generation more dramatically than any other: Climate change. The millions of young people worldwide who've organized and joined today's #ClimateStrike demand action to protect our planet, and they deserve it.
So it looks like someone simply edited a local copy of that tweet to modify the text and the date before uploading a manipulated screenshot to Reddit as a joke, after which it "escaped" and went viral on the internet where many people thought it was real.