Hanging quotes on iOS 7.Basically, we set the UITextView's left inset to the negative width of a double quote, then undo that per line fragment if the line doesn't start with a double quote.And the opposite for an exclusion path lines.

WPHangingQuoteViewController.m

- (void)loadOrResizeOrSometing {
    /*
     *  After creating the text view or resizing the font, set the quoteWidth and contentInset.
     */
    WPTextContainer *textContainer = (WPTextContainer*)paragraphView.textContainer;
    textContainer.spaceWidth = [self widthForCharacter:@" "];
    textContainer.charWidths = @{
                                 @(8220) : @([self widthForCharacter:@"“"]),
                                 @(8216) : @([self widthForCharacter:@"‘"]),
                                 @('"')  : @([self widthForCharacter:@"\""]),
                                 @('\'') : @([self widthForCharacter:@"'"]),
                                 @(8226) : @([self widthForCharacter:@"•"]),
                                 @(9679) : @([self widthForCharacter:@"●"])
                                };

    CGFloat maxCharWidth = [[textContainer.charWidths.allValues valueForKeyPath:@"@max.self"] floatValue];
    CGFloat insetWidth = ceilf(maxCharWidth + textContainer.spaceWidth);
    paragraphView.contentInset = UIEdgeInsetsMake(0, -insetWidth, 0, 0);
    paragraphView.textContainerInset = UIEdgeInsetsZero;
}

- (CGFloat)widthForCharacter:(NSString*)charater {
    CGRect rect = [charater boundingRectWithSize:CGSizeMake(CGFLOAT_MAX, CGFLOAT_MAX)
                                         options:0
                                      attributes:@{ NSFontAttributeName: yourTextViewFont }
                                         context:nil];
    return rect.size.width;
}

WPTextContainer.h

//
//  WPTextContainer.h
//  WashPost
//
//  Created by Moore, Stuart on 1/16/14.
//  Copyright (c) 2014 Washington Post. All rights reserved.
//

#import <UIKit/UIKit.h>

@interface WPTextContainer : NSTextContainer

@property (nonatomic, weak) UITextView *view;
@property (nonatomic, strong) NSDictionary *charWidths;
@property (nonatomic, assign) CGFloat spaceWidth;

@end

WPTextContainer.m

//
//  WPTextContainer.m
//  WashPost
//
//  Created by Moore, Stuart on 1/16/14.
//  Copyright (c) 2014 Washington Post. All rights reserved.
//

#import "WPTextContainer.h"

@implementation WPTextContainer

- (instancetype)initWithSize:(CGSize)size {
    if(self = [super initWithSize:size]) {
        self.lineFragmentPadding = 0;
        self.widthTracksTextView = YES;
    }
    return self;
}

- (CGRect)lineFragmentRectForProposedRect:(CGRect)proposedRect
                                  atIndex:(NSUInteger)index
                         writingDirection:(NSWritingDirection)direction
                            remainingRect:(CGRect*)remainingRect {
    
    CGRect rect = [super lineFragmentRectForProposedRect:proposedRect
                                                 atIndex:index
                                        writingDirection:direction
                                           remainingRect:remainingRect];
    
    NSString *string = self.layoutManager.textStorage.string;
    
    if(string.length > 0 && index < string.length) {
        unichar character = [string characterAtIndex:index];
        CGFloat charWidth = [self.charWidths[@(character)] floatValue];
        
        if(charWidth) {
            CGFloat width = charWidth;
            
            if((index+1) < string.length &&
               ([string characterAtIndex:(index+1)] == ' ' ||
                [string characterAtIndex:(index+1)] == 160 /* &nbsp; */))
                width += self.spaceWidth;
            
            if(![self isOffsetByExclusionPath:rect.origin.x])
                rect.origin.x = -self.view.contentInset.left - width;
            else
                rect.origin.x -= width;
            
            rect.size.width = self.size.width - rect.origin.x;
        } else if(![self isOffsetByExclusionPath:rect.origin.x]) {
            rect.origin.x = -self.view.contentInset.left;
            rect.size.width = self.size.width - rect.origin.x;
        }
    }
    
    return CGRectIntegral(rect);
}

- (BOOL)isOffsetByExclusionPath:(CGFloat)x {
    return (BOOL)(x > -self.view.contentInset.left);
}

@end