The correct spelling is “veteran” for a person with long experience or service. The plural is “veterans” (e.g., veterans day). The form “veteren” is incorrect in English. If you’re unsure about capitalization or hyphenation in a specific context, here are quick checks:

• Use “veteran” when referring to a person who has long experience or who has served in the armed forces.
• Use “Veterans Day” when naming the U.S. holiday or similar proper noun contexts.
• In adjectival use, you can say “veteran athlete,” “veteran worker,” etc.