Hours which are past midnight are suffixed with next day date. In Panchang day starts and ends with sunrise.
Each lunar month in Hindu calendar has two Chaturthi Tithis. According to Hindu scriptures Chaturthi Tithi(s) belongs to Lord Ganesha. The Chaturthi after Amavasya or new moon during Shukla Paksha is known as Vinayaka Chaturthi and the one after Purnimasi or full moon during Krishna Paksha is known as Sankashti Chaturthi.
Although Vinayaka Chaturthi fasting is done every month but the most significant Vinayaka Chaturthi falls in month of Bhadrapada. Vinayaka Chaturthi during Bhadrapada month is known as Ganesha Chaturthi. Ganesha Chaturthi is celebrated by Hindus all over the world as the birthday of Lord Ganesha.
Vinayaka Chaturthi is also known as Varad Vinayaka Chaturthi. Varad means "asking God to fulfill any desire one has". Lord Ganesha blesses devotees with wisdom and patience who observe this fast. The wisdom and patience are two virtues whose significance is known to human kind since ages. Anyone who possesses these virtues can progress in life and can achieve whatever one desires.
Ganesha Puja on Vinayaka Chaturthi is done during afternoon which is midday according to Hindu calendar. The Muhurta to worship lord Ganesha during afternoon is listed along with Vinayaka Chaturthi dates.
It is important to understand that fasting day for Vinayaka Chaturthi might differ for two cities even if those cities are within same Indian state. Fasting for Vinayaka Chaturthi depends on sunrise and sunset timings and it is observed when Chaturthi Tithi prevails during midday. Hence Vinayaka Chaturthi fasting might be observed on Tritiya Tithi i.e. one day before Chaturthi Tithi. As midday time depends on sunrise and sunset, which are different for all cities, it is important to refer Hindu calendar like this website which lists location based Vinayaka Chaturthi days. As generating location based dates are time consuming most sources ignore this fact and publish single list for all Indian cities.