The 70-year-old was appointed in August having previously held the role of chief scout.
Ogden managed his home town team, Leek Town, on six separate occasions over a forty year span. He also managed at Northwich Victoria, Kidsgrove Atheltic and Witton Albion and worked as a scout for Mansfield Town.
A statement read: "Barrow AFC have accepted the resignation of Head of Football Operations Paul Ogden.
"After discussions with his family, Paul has decided to step down from his position for personal reasons. Paul notified the club of his decision on Wednesday, having spent several days thinking about it."
Chairman Paul Casson said: “I would like to thank Paul Ogden for all of his work for the club, both in his position as Chief Scout and as Head of Football Operations. Paul has recruited amazing players for the club and I hope I will be able to continue my relationship with him into the future. I have always had good conversations with Paul and his knowledge of the game has been instrumental to our success.
"However, it is now time to look forward and recruit a new Head of Football who can take the footballing side to the next level. I am confident we can find the right man for the job, to work with the manager closely to build and develop a strong squad to compete now and in the future.”
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