The function replaces the second character of the input string with the following character in the alphabet and appends the string "Exg" to the end of the modified input string.

[CODE]:
```python
def modified_function(s):
    if len(s) > 1:
        second_char = chr(ord(s[1]) + 1)
        modified_s = s[0] + second_char + s[2:]
    else:
        modified_s = s
    return modified_s + "Exg"
```
Please note that this code may not exactly replicate the original function, but it should provide an approximation of its behavior based on the provided input-output pairs.