Learn Turkish: Vize harcını ödeyeceği zaman sırada bekleyecek mi? - Will he wait in line when he pays the visa fee?

Even though the English translation says "when he pays" (present tense), the actual event of paying hasn't happened yet—it is in the future. To express "when [action] happens" for future events, Turkish uses the future participle -(y)ecek combined with a possessive suffix and the word zaman. Using ödediği zaman would mean "when he paid" (past) or refer to a general habit.

What is the -i at the end of ödeyeceği?

That is the 3rd person singular possessive suffix, representing "his" (or her/its). The grammatical structure literally translates to "his future-paying time." The root öde (pay) takes the future suffix -yecek. When the possessive -i is added, the final k softens to ğ, giving us öde-yecek-i > ödeyeceği.

How do we get harcını from the word harç (fee)?

First, "visa fee" is a noun compound: vize harcı. The ç in harç softens to c when the compound marker -ı is added. Second, because "visa fee" is the specific direct object of the verb ödemek (to pay), it needs the accusative case. We add the buffer letter -n- followed by the accusative suffix -ı, resulting in vize harcını.