Middle of state hit by old battle (5)
I believe the answer is:
alamo
'battle' is the definition.
(famous mission and siege from the Texas revolution)
'middle of state hit by old' is the wordplay.
'middle of' says to take the centre.
'hit' becomes 'lam' (to 'lam' means to hit hard).
'by' is a charade indicator (letters next to each other).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
The middle letter of 'state' is 'a'.
'a'+'lam'+'o'='ALAMO'
(Other definitions for alamo that I've seen before include "Famous Texan mission" , "Mission building in Texas, site of famous siege by Mexico" , "The --, Texan mission besieged in 1836" , "Site of 1836 massacre in Texas" , "Where Davy Crockett died, 1836" .)