来着 is used as an auxiliary word of tense at the end of a sentence indicating a completed action. In this case, 着 is pronounced in the neutral tone zhe.
Examples:
你刚才说什么来着？ nǐ gāng cái shuō shí me lái zhe ？What were you saying just now?
你昨天让我买什么来着？nǐ zuó tiān ràng wǒ mǎi shí me lái zhe ？What did you ask me to buy yesterday?
你刚才用我不懂的话跟他说什么来着？nǐ gāng cái yòng wǒ bú dǒng de huà gēn tā shuō shí me lái zhe ？What did you say to him in the unknown tongue?
他新近又见她来着，他先征求我的同意，好再跟她求婚。tā xīn jìn yòu jiàn tā lái zhe ，tā xiān zhēng qiú wǒ de tóng yì ，hǎo zài gēn tā qiú hūn 。He has seen her lately, and has asked me for permission to pay his addresses to her.
是谁摆弄这钟来着? 已经不走了。shì shuí bǎi nòng zhè zhōng lái zhe ? yǐ jīng bú zǒu le. Who’s been interfering with the clock? It’s stopped.
我记不得玛丽昨天下午在做什么来着。wǒ jì bú dé mǎ lì zuó tiān xià wǔ zài zuò shí me lái zhe 。I can’t remember what Mary was doing yesterday afternoon.
You can check more example sentences of 来着
Attention：
When 来着 is used as an auxiliary word to indicate a completed action, neither 过 nor 了 can be used in the same sentence. As you can see in the example sentences above, neither 过 nor 了 is used. That’s because either 过 or 了 indicates a completed action too. However, 过 and 了 can be used in the same sentence, for example, 我去过纽约了 I have been to New York.
To remember this point, we have an interesting tip: 来着 is a combination of two characters and is not single any more. So it doesn’t like to stay with anyone more. 过 and 了 are both single, and they like staying together sometimes.
See the auxiliary words