Note : If you increase App or Device storage space of Xperia C then your Internal Memory becomes 210 MB, therefore members you do not have memory card yet should not proceed with this tutorial to increase app storage space of Xperia C.

1. Important : First of all Take Full CWM backup of Xperia C, by booting into recovery and selecting Backup and Restore and then selecting backup using power button. This is needed because in the process of Increasing App storage space of Xperia C, your full data will be lost and therefore you need CWM Backup to restore to the point you took the backup. If you do not have CWM Recovery Installed, then read this : Install Pure CWM on Xperia C and then proceed. Any other recovery like Carliv or TWRP can also work. 
2. Now download Increase Apps Storage Space of Xperia C file from  Download Increase Apps Storage.zip It is flashable zip file. One must place the downloaded zip file to SD card or any other location you remember.
3. Now boot into recovery and flash the downloaded file using Install ZIP from SD card.
4.  Once installation is finished, then restart your Xperia C. 
5. Xperia C will take almost 10 minutes in rebooting, Please Do not get panic, as we have already tested the same and found it working on Xperia C. 
6. Once Xperia C starts, then simply turn off the phone and again boot into recovery and restore the backup you created earlier using CWM. By this you will restore all the data you had earlier.

You are done in increasing the Memory space of the Apps storage of Xperia C. Thanks to Merabi Machavariani for trying it and also giving information.