I found a gold ring in my pool. More than a month has passed since I announced finding it. What should I do now?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

This ring now under your care is considered among those lost items found by someone but the rightful owner is unknown. The ruling of such a thing in Shari'a is that the person who picked it up should make public announcement of finding it for one year. The announcement should be made where people gather, such as markets, near mosques and other public places. One may even publish the news in a daily paper. The found item is considered as being on deposit, so the finder is not responsible if something accidentally happens to it. However, if he trespasses his limits or is neglectful then he becomes responsible for failure to discharge his duty.
When the owner comes to establish his ownership and describes the item correctly he will take possession of it. If one year passes and no one claims ownership then the finder can give it in charity or utilize it as he wishes, whether he is rich or poor. If after he uses or gives it in charity the original owner appears and approves of those acts, there is no harm. If he still demands his property, he should be paid its price.
The evidence for the above details is the Hadith of Zaid bin Khalid the prophet said: "Make public announcement about it for one year. Remember the description of its container and the string with which it is tied; and if somebody comes and claims it and describes it correctly, (give it to him); otherwise, utilize it" .
Allah knows best.