UICollectionView Cell Scroll to centre

you can use code self.collectionView.scrollToItem(at: indexPath, at: .centeredHorizontally, animated: true)

You can override targetContentOffsetForProposedContentOffset:withScrollingVelocity: method in your UICollectionViewLayout subclass and calculate your offset there like this:

@property (nonatomic, assign) CGFloat previousOffset;
@property (nonatomic, assign) NSInteger currentPage;

...

- (CGPoint)targetContentOffsetForProposedContentOffset:(CGPoint)proposedContentOffset withScrollingVelocity:(CGPoint)velocity {
    NSInteger itemsCount = [self.collectionView.dataSource collectionView:self.collectionView numberOfItemsInSection:0];

    // Imitating paging behaviour
    // Check previous offset and scroll direction
    if ((self.previousOffset > self.collectionView.contentOffset.x) && (velocity.x < 0.0f)) {
        self.currentPage = MAX(self.currentPage - 1, 0);
    } else if ((self.previousOffset < self.collectionView.contentOffset.x) && (velocity.x > 0.0f)) {
        self.currentPage = MIN(self.currentPage + 1, itemsCount - 1);
    }

    // Update offset by using item size + spacing
    CGFloat updatedOffset = (self.itemSize.width + self.minimumInteritemSpacing) * self.currentPage;
    self.previousOffset = updatedOffset;

    return CGPointMake(updatedOffset, proposedContentOffset.y);
}

EDIT: thanks for pointing this out, forgot to say that you have to disable paging first:

self.collectionView.pagingEnabled = NO;

UPDATE: attaching Swift 4.2 version

...
collectionView.isPagingEnabled = false
...

class YourCollectionLayoutSubclass: UICollectionViewFlowLayout {

    private var previousOffset: CGFloat = 0
    private var currentPage: Int = 0

    override func targetContentOffset(forProposedContentOffset proposedContentOffset: CGPoint, withScrollingVelocity velocity: CGPoint) -> CGPoint {
        guard let collectionView = collectionView else {
            return super.targetContentOffset(forProposedContentOffset: proposedContentOffset, withScrollingVelocity: velocity)
        }

        let itemsCount = collectionView.numberOfItems(inSection: 0)

        // Imitating paging behaviour
        // Check previous offset and scroll direction
        if previousOffset > collectionView.contentOffset.x && velocity.x < 0 {
            currentPage = max(currentPage - 1, 0)
        } else if previousOffset < collectionView.contentOffset.x && velocity.x > 0 {
            currentPage = min(currentPage + 1, itemsCount - 1)
        }

        // Update offset by using item size + spacing
        let updatedOffset = (itemSize.width + minimumInteritemSpacing) * CGFloat(currentPage)
        previousOffset = updatedOffset

        return CGPoint(x: updatedOffset, y: proposedContentOffset.y)
    }
}