Which letter cluster will replace the question mark ($?$) to complete the given series?
TWEZ, XBYG, ?, FLMU, JQGB

Let's evaluate the shift pattern for each letter position independently:
1. First Letter:
T (20) $\stackrel{+4}{\to }$ X (24) $\stackrel{+4}{\to }$ B (2) $\stackrel{+4}{\to }$ F (6) $\stackrel{+4}{\to }$ J (10)
2. Second Letter:
W (23) $\stackrel{+5}{\to }$ B (2) $\stackrel{+5}{\to }$ G (7) $\stackrel{+5}{\to }$ L (12) $\stackrel{+5}{\to }$ Q (17)
3. Third Letter:
E (5) $\stackrel{-6}{\to }$ Y (25) $\stackrel{-6}{\to }$ S (19) $\stackrel{-6}{\to }$ M (13) $\stackrel{-6}{\to }$ G (7)
4. Fourth Letter:
Z (26) $\stackrel{+7}{\to }$ G (7) $\stackrel{+7}{\to }$ N (14) $\stackrel{+7}{\to }$ U (21) $\stackrel{+7}{\to }$ B (2)

Combining all the positions, the missing letter cluster is BGSN.