Which browser engine began as Apple’s fork of KHTML and KJS? WebKit. Apple based WebKit on KHTML, KDE’s HTML layout engine, and KJS, its companion JavaScript engine. The work began around 2001 as Apple adapted the KDE components for Mac OS X and its upcoming Safari browser.
Apple renamed the adapted rendering component WebCore and the JavaScript component JavaScriptCore, while the wider browser technology became known as WebKit. Apple later open-sourced major parts of the project, allowing it to become a broadly used platform beyond Safari.
A common mix-up is Blink. Google forked WebCore from WebKit in 2013 to create Blink, which became the engine used by Chromium and Chrome. Blink is therefore a descendant of WebKit, not the engine that originally began as Apple’s KHTML/KJS fork. KHTML itself originated in KDE’s Konqueror project.