To solve this coding problem, we will analyze how each letter is transformed in the given examples. The problem states:

• 'FIT' is coded as 'FGIST'.
• 'KIN' is coded as 'KLIMN'.

We must determine how 'JOY' will be written in this code language.

Let's break down the pattern:

1. For the word 'FIT' to 'FGIST':
   • The first letter 'F' remains unchanged.
   • A letter 'G' (the next alphabetic character after 'F') is inserted.
   • The letter 'I' remains unchanged.
   • A letter 'S' (the next alphabetic character after 'I') is inserted.
   • The letter 'T' remains unchanged.
2. For the word 'KIN' to 'KLIMN':
   • The first letter 'K' remains unchanged.
   • A letter 'L' (the next alphabetic character after 'K') is inserted.
   • The letter 'I' remains unchanged.
   • A letter 'M' (the next alphabetic character after 'I') is inserted.
   • The letter 'N' remains unchanged.

From these observations, the pattern is clear: for each existing letter in the word, the letter itself is followed by its subsequent letter in the alphabet.

Now, let's apply this pattern to 'JOY':

1. 'J' becomes 'JK' (J is followed by the next letter K).
2. 'O' becomes 'OX' (O is followed by the next letter P).
3. 'Y' stays as it is since it is already the last letter, no following insertion.

Therefore, 'JOY' in this code language is written as 'JKOXY'.

Thus, the correct answer is JKOXY.