Is there a way to change the text position in UITabBar or UITabBarItem?

You probably want to apply this offset globally, so I'd suggest

Obj-C

[UITabBarItem appearance].titlePositionAdjustment = UIOffsetMake(0, -4);

Swift:

UITabBarItem.appearance().titlePositionAdjustment = UIOffset(horizontal: 0, vertical: -4)

Why don't you just have an empty title property for your view controller and add the title to your custom images for the tab?

UPDATE: For the sake of completeness of answer; from comments and ios tabbar put text in the middle when no image

[tab.tabBarItem setTitlePositionAdjustment:UIOffsetMake(0, -10)]

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