Is the transistor Q4 in the wide swing cascode current mirror operating in linear region?
\$V_{D4} = V_t + V_{OV} \$

\$V_{G4} = V_t + 2V_{OV} \$

\$V_{S4} = V_{OV} \$

.

Hence:

\$V_{GS4} = V_{G4} - V_{S4} = V_t + 2V_{OV} - V_{OV} = V_t + V_{OV}\$

\$V_{DS4} = V_{D4} - V_{S4} = V_t + V_{OV} - V_{OV} = V_t\$

.

Q4 is in saturation if:

\$V_{DS4} &gt;= V_{GS4} - V_t\$

what leads to:

\$V_t &gt;= V_t + V_{OV} - V_t\$

\$V_t &gt;= V_{OV}\$

.

Hence

A) if \$V_t &gt;= V_{OV}\$ then Q4 in a saturation

B) if \$V_t &lt; V_{OV}\$ then Q4 in a linear region


  Is it not necessary for transistor to operate in saturation region?


No. See explanation below.


  Is it ok to operate in linear region as I am not finding any issue?


Yes, it is ok for a transistor to operate in a linear region. Depends on the situation. Generally, during designing you try to have saturation in all transistors due to e.g. high output impedance. However, you may want some of your transistors to operate in linear region due to their functions (e.g. resistor behavior) or there is no big difference between behavior of a given transistor between linear or saturation region for a given situation or linear region may be forced by the architecture as is in the case of your current mirror.