Kafka had a day job and a writing life, and the only way he could fit both was to push the writing into the dark hours. He started around eleven at night and worked until the small hours. Some nights he didn't stop until dawn.

The Direct Answer
Kafka wrote late at night, usually from about 11pm onward.
He'd go on “until one, two, or three o'clock, once even till six in the morning,” per his Letters to Felice.

The Day Came First

From 1908 Kafka worked at the Workers' Accident Insurance Institute in Prague, and he was lucky to land the single-shift schedule. That meant office hours of roughly 8 or 8:30 in the morning until 2 or 2:30 in the afternoon. Most colleagues worked a longer split day, so his early finish was a genuine privilege. Even so, by the time he got home the part of the day a writer would normally use was already spent on insurance reports.

So he restructured everything around the night. First lunch, then a long nap that could run as much as four hours. Then a bit of exercise, a walk, dinner with the family. None of that was idleness. It was the slow climb-down from the office that let him reach the desk in something like the right state. Only after all of it, with the apartment finally quieting, did he start to write.

Eleven O'Clock and After

In a letter to Felice Bauer he laid out the timetable plainly. He'd begin around eleven and keep going as long as he could hold up, “depending on my strength, inclination, and luck, until one, two, or three o'clock, once even till six in the morning.” Then he'd sleep for a few hours and head back to the office. The math is brutal, and Kafka knew it. He told Felice the present way was the only possible one, and that if he couldn't bear it, so much the worse, but he'd bear it somehow.

The drained, sleep-starved version of him that showed up to work was the price of every page. He paid it for years and complained about it the whole time, yet he never reversed the arrangement. The night kept the writing alive.

It's worth noticing what the schedule does and doesn't prove. Kafka often blamed the office for his blocked, stalled stretches, and his biographers have pushed back on that, pointing out that he also wasted plenty of the free time he did have. The late hours were real and the exhaustion was real. They just didn't guarantee output. Some of those nights produced masterpieces. Many produced a few labored sentences and a long diary complaint about how little he'd managed.

This story, 'The Judgment,' I wrote at one sitting during the night of the 22nd-23rd, from ten o'clock at night to six o'clock in the morning.

Franz Kafka, Diaries, September 23, 1912

He came to believe the night wasn't merely convenient. It was necessary. The darkness and the silence let him drop into the work completely, and he was convinced that writing done any other way came out thinner. Worth saying plainly: a fair amount of these late hours went to letters and his diary rather than fiction, so the legend of nonstop production needs a little trimming. For the wider picture, see the full Franz Kafka writing routine.

What You Can Steal