was there slavery in this dynasty?
Yes, Slaves comprised roughly 1% of the population.
Society and culture of the Han dynasty
Slaves ("nuli" 奴隸) comprised roughly 1% of the population, a proportion far less than the contemporary Greco-Roman world which relied on the labor of a large slave population. Slaves were classified into two categories: those who were privately owned, and those who were owned by the state. Privately owned slaves were often former peasants who fell into debt and sold themselves into slavery, while others were former government slaves bestowed to nobles and high officials as rewards for their services.
who was valued in han society under the philosophy of confucianism Emperor Gaozu of Han. can you mention few names of people of the royal family? Emperor Zhao (r. 87–74 BCE) , Emperor Yuan (r. 48–33 BCE)  Emperor Cheng (33–7 BCE) ,  Emperor He (r. 88–105 CE) ,  Emperor Shun (r. 125–144 CE) , Emperor Ling (r. 168–189 CE).
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Society and culture of the Han dynasty [SEP] Slaves
Slaves ("nuli" 奴隸) comprised roughly 1% of the population, a proportion far less than the contemporary Greco-Roman world which relied on the labor of a large slave population. Slaves were classified into two categories: those who were privately owned, and those who were owned by the state. Privately owned slaves were often former peasants who fell into debt and sold themselves into slavery, while others were former government slaves bestowed to nobles and high officials as rewards for their services. State-owned slaves were sometimes prisoners of war (yet not all were made slaves). However, most slaves were tributary gifts given to the court by foreign states, families of criminals who committed treason against the state, and former private slaves who were either donated to authorities (since this would exempt the former slaveholder from labor obligations) or confiscated by the state if their master had broken a law.