Hi Dhiren,
Again, I apologize for taking so long to respond. It looks to me like you have made the proper connections to your schematic for the AVDD/AVSS power supply connections. You asked about using the internal temperature sensor of the ADS1148 for the CJC. The temperature sensor for the ADS1148 is not good enough to use for that purpose. As far as using the LM334, I don't understand your connections. Bascically you have a current source and no load or set point for the current. You might want to revisit that connection to make sure you have it correct.
When using bipolar supplies (+/-2.5V) VBIAS will be at AGND. If your sensor has a connection to AGND, then you do not need to turn on VBIAS.
Check again your register settings. MUX0 setting of 0x41 is AIN0 connected to AINP and AIN1 connected to AINN, as well as burnout current source on at 0.5uA. Leaving the BCS on while making your TC measurement will add error both in terms of self heating and also with voltage drops across the filter components. VBIAS on may not be necessary. MUX1 settings are appropriate. SYS0 (you call PGA) appear to be appropriate.
Best regards,
Bob B