Some people consider first thirteen days of safar as inauspicious and called them as TERA-TEZI.
It there any hadith in support of this or it is just a superstition.
First of all: I've never heard about the 13 unlucky days of Safar.
Second of all: Some muslims, especially Shia, consider both Muharram and Safar months of grief and sadness, that's because Muharram is the month which Husain ibn Ali was killed in the famous Battle of Karbala, and a lot of other Wafiyat (deaths) happened in this two months, including:
10 Muharram 61h: death of Imam husain and his friends and most of his family in the Battle of Karbala
13 Muharram: burial of the Imam and his friends by Bani Asad after 3 days of the battle.
25 Muharram 95d: death of Imam Ali ibn Husain.
3 Safar: death of Zaid ibn Ali ibn Abi Talib.
7 Safar 50h: death of Imam Hasan ibn Ali, the brother of Imam Husain and the son of Ali.
8 Safar 35h: death of Salman Al-Farisi (A.k.a Salman the Persian, Salman Al-Muhammadi).
9 Safar 50h: death of Ammar ibn Yasir.
14 Safar 35h: death of Muhammad ibn Abi Bakr.
17 Safar 50h: death of Imam Ali Al-Ridha.
20 Safar: The Arbaeen.
25 Safar: death of Mariam bint Imran.
28 Safar: death of Prophet Muhammad and Imam Has ibn ibn Ali (another source).
There is NOTHING like Un-lucky or suspicious about this month. and dont go for people, people believe in millions of stupid actions, you cannot just follow them in everything. if you do, they will lead you to hellfire.
Coming to the question, here is the hadith to prove that this month has nothing like this superstition:
The Prophet (sallallaahu ‘alayhi wasallam) said,
“There is no contagious disease that is transferred except by Allaah's permission. Nor is there the belief of when seeing or hearing an owl that it is the announcement of someone's death. Nor is there the belief of being pessimistic about the month of Safar. And fear the leper like you fear a lion.'
for detailed answer, you can go here: http://www.almuflihoon.com/index.php?option=com_content&view=article&id=103:the-month-of-safar-and-bad-omens-&catid=38:innovations&Itemid=142