Uthman performed four units of prayer at Mina only because he had resolved to settle there after the Hajj.
حدثنا محمد بن العلاء أخبرنا ابن المبارك عن معمر
أن عثمان إنما صلى بمنى أربعا لأنه أجمع على الإقامة بعد الحج
No references are available.
[Its isnad is daif] The chain is disconnected, since Zuhri did not meet Uthman, may Allah be pleased with him.