Which work has been called by Shakespeare as, "the first heir of my invention'?

Option 3 : Venus and Adonis

The correct answer is Venus and Adonis. 

• Venus and Adonis is a narrative poem by William Shakespeare published in 1593. It is arguably Shakespeare's first publication. 
• It is written in stanzas of six lines of iambic pentameter rhyming ABABCC. Although this verse form was known before Shakespeare's use, it is now commonly known as the Venus and Adonis stanza, after this poem. 
• It was published originally as a quarto pamphlet and published with great care.
• The poem is inspired by and based on stories found in the Metamorphoses, a narrative poem by the Latin poet, Ovid, although Shakespeare's version is greatly different from that of Ovid. 
• The poem begins with a brief dedication to Henry Wriothesley, 3rd Earl of Southampton, in which the poet describes the poem as "the first heir of my invention". Thus we understand that the correct answer is Venus and Adonis. 

Therefore, Option 3 is the correct answer.

• The poem tells the story of Venus, the goddess of Love and of her attempted seduction of Adonis, an extremely handsome young man, who would rather go hunting. 
• The poem is pastoral, and at times erotic, comic and tragic. It contains discourses on the nature of love, and observations on nature. 
• It has certain stylistic qualities in common with A Midsummer Night's Dream, Romeo and Juliet, and Love's Labour's Lost. It was written when the London theatres were closed for a time due to the bubonic plague. 

• Hero and Leander is a poem by Christopher Marlowe that retells the Greek myth of Hero and Leander. After Marlowe's untimely death it was completed by George Chapman. Two editions of the poem were issued in quarto in 1598. 
• The Rape of Lucrece (1594) is a narrative poem by William Shakespeare about the legendary Roman noblewoman Lucretia. In his previous narrative poem, Venus and Adonis (1593), Shakespeare had included a dedicatory letter to his patron, the Earl of Southampton, in which he promised to compose a "graver labour". Accordingly, The Rape of Lucrece has a serious tone throughout. 
• The Comedy of Errors is one of William Shakespeare's early plays. It is his shortest and one of his most farcical comedies, first performed sometime in 1595.