// LCD module connections
sbit LCD_RS at RB2_bit;
sbit LCD_EN at RB3_bit;
sbit LCD_D4 at RB4_bit;
sbit LCD_D5 at RB5_bit;
sbit LCD_D6 at RB6_bit;
sbit LCD_D7 at RB7_bit;
sbit LCD_RS_Direction at TRISB2_bit;
sbit LCD_EN_Direction at TRISB3_bit;
sbit LCD_D4_Direction at TRISB4_bit;
sbit LCD_D5_Direction at TRISB5_bit;
sbit LCD_D6_Direction at TRISB6_bit;
sbit LCD_D7_Direction at TRISB7_bit;
// End LCD module connections
 
unsigned short read_ds1307(unsigned short address)
{
  unsigned short r_data;
  I2C1_Start();
  I2C1_Wr(0xD0); //address 0x68 followed by direction bit (0 for write, 1 for read) 0x68 followed by 0 --> 0xD0
  I2C1_Wr(address);
  I2C1_Repeated_Start();
  I2C1_Wr(0xD1); //0x68 followed by 1 --> 0xD1
  r_data=I2C1_Rd(0);
  I2C1_Stop();
  return(r_data);
}

void write_ds1307(unsigned short address,unsigned short w_data)
{
  I2C1_Start(); // issue I2C start signal
  //address 0x68 followed by direction bit (0 for write, 1 for read) 0x68 followed by 0 --> 0xD0
  I2C1_Wr(0xD0); // send byte via I2C (device address + W)
  I2C1_Wr(address); // send byte (address of DS1307 location)
  I2C1_Wr(w_data); // send data (data to be written)
  I2C1_Stop(); // issue I2C stop signal
}

unsigned char BCD2UpperCh(unsigned char bcd)
{
  return ((bcd >> 4) + '0');
}

unsigned char BCD2LowerCh(unsigned char bcd)
{
  return ((bcd & 0x0F) + '0');
}

int Binary2BCD(int a)
{
  int t1, t2;
  t1 = a%10;
  t1 = t1 & 0x0F;
  a = a/10;
  t2 = a%10;
  t2 = 0x0F & t2;
  t2 = t2 << 4;
  t2 = 0xF0 & t2;
  t1 = t1 | t2;
  return t1;
}
 
int BCD2Binary(int a)
{
  int r,t;
  t = a & 0x0F;
  r = t;
  a = 0xF0 & a;
  t = a >> 4;
  t = 0x0F & t;
  r = t*10 + r;
  return r;
}

int second;
int minute;
int hour;
int hr;
int day;
int dday;
int month;
int year;
int ap;

unsigned short set_count = 0;
short set;
 
char time[] = "00:00:00 PM";
char date[] = "00-00-00";

void main()
{
  I2C1_Init(100000); //DS1307 I2C is running at 100KHz
  CMCON = 0x07;   // To turn off comparators
  ADCON1 = 0x06;  // To turn off analog to digital converters
  TRISA = 0x07;
  PORTA = 0x00;
  Lcd_Init();                        // Initialize LCD
  Lcd_Cmd(_LCD_CLEAR);               // Clear display
  // Lcd_Cmd(_LCD_CURSOR_OFF);          // Cursor off
  Lcd_Cmd(_LCD_BLINK_CURSOR_ON);
  Lcd_out(1,1,"Time:");
  Lcd_out(2,1,"Date:");

  do
  {
    set = 0;
    if(PORTA.F0 == 0)
    {
      Delay_ms(100);
      if(PORTA.F0 == 0)
      {
        set_count++;
        if(set_count >= 7)
        {
          set_count = 0;
        }
      }
    }
    if(set_count)
    {
      if(PORTA.F1 == 0)
      {
        Delay_ms(100);
        if(PORTA.F1 == 0)
          set = 1;
      }
      if(PORTA.F2 == 0)
      {
         Delay_ms(100);
         if(PORTA.F2 == 0)
           set = -1;
      }
      if(set_count && set)
      {
        switch(set_count)
        {
          case 1:
                  hour = BCD2Binary(hour);
                  hour = hour + set;
                  hour = Binary2BCD(hour);
                  if((hour & 0x1F) >= 0x13)
                  {
                    hour = hour & 0b11100001;
                    hour = hour ^ 0x20;
                  }
                  else if((hour & 0x1F) <= 0x00)
                  {
                     hour = hour | 0b00010010;
                     hour = hour ^ 0x20;
                  }
                  write_ds1307(2, hour); //write hour
                  break;
          case 2:
                  minute = BCD2Binary(minute);
                  minute = minute + set;
                  if(minute >= 60)
                    minute = 0;
                  if(minute < 0)
                    minute = 59;
                  minute = Binary2BCD(minute);
                  write_ds1307(1, minute); //write min
                  break;
          case 3:
                  if(abs(set))
                  write_ds1307(0,0x00); //Reset second to 0 sec. and start Oscillator
                  break;
          case 4:
                  day = BCD2Binary(day);
                  day = day + set;
                  day = Binary2BCD(day);
                  if(day >= 0x32)
                    day = 1;
                  if(day <= 0)
                    day = 0x31;
                  write_ds1307(4, day); // write date 17
                  break;
          case 5:
                  month = BCD2Binary(month);
                  month = month + set;
                  month = Binary2BCD(month);
                  if(month > 0x12)
                    month = 1;
                  if(month <= 0)
                    month = 0x12;
                  write_ds1307(5,month); // write month 6 June  
                  break;
          case 6:
                  year = BCD2Binary(year);
                  year = year + set;
                  year = Binary2BCD(year);
                  if(year <= -1)
                    year = 0x99;
                  if(year >= 0x50)
                    year = 0;
                  write_ds1307(6, year); // write year
                  break;
        }

      }
    }

    second = read_ds1307(0);
    minute = read_ds1307(1);
    hour = read_ds1307(2); 
    hr = hour & 0b00011111; 
    ap = hour & 0b00100000;
    dday = read_ds1307(3);
    day = read_ds1307(4);
    month = read_ds1307(5);
    year = read_ds1307(6);

    time[0] = BCD2UpperCh(hr);
    time[1] = BCD2LowerCh(hr);
    time[3] = BCD2UpperCh(minute);
    time[4] = BCD2LowerCh(minute);
    time[6] = BCD2UpperCh(second);
    time[7] = BCD2LowerCh(second);

    date[0] = BCD2UpperCh(day);
    date[1] = BCD2LowerCh(day);
    date[3] = BCD2UpperCh(month);
    date[4] = BCD2LowerCh(month);
    date[6] = BCD2UpperCh(year);
    date[7] = BCD2LowerCh(year);

    if(ap)
    {
      time[9] = 'P';
      time[10] = 'M';
    }
    else
    {
      time[9] = 'A';
      time[10] = 'M';
    } 
    Lcd_out(1, 6, time);
    Lcd_out(2, 6, date);
    Delay_ms(100);
  }while(1);
}

You can find that all bits of HOUR registers are not used for indicating hour magnitude. It can indicate in 24 or 12 hour mode.