It seems like you're referring to Bose on-ear headphones, which are a popular choice among audio enthusiasts for their combination of comfort, sound quality, and advanced features. Bose offers several models of on-ear headphones, each designed to cater to different user preferences and requirements. Here's a brief overview of some notable on-ear headphones from Bose:

1. **Bose QuietComfort 35 II Wireless Headphones**: Although primarily known as over-ear headphones, the QC35 II can also be considered on-ear for users with smaller ears or head sizes, as the ear cups may not fully enclose the ears. These headphones offer industry-leading noise cancellation technology, allowing you to enjoy your music or podcasts in peace, even in noisy environments. They feature Bluetooth connectivity, voice assistant integration (Amazon Alexa, Google Assistant), and a 20-hour battery life.

2. **Bose SoundLink On-Ear Wireless Headphones**: Designed specifically for on-ear wear, these headphones provide balanced audio performance and a lightweight, comfortable fit. They offer wireless freedom through Bluetooth connectivity, a 15-hour battery life, and a built-in microphone for hands-free calls. The SoundLink headphones also have easy-to-use controls and a foldable design for convenient storage and portability.

3. **Bose SoundTrue Ultra In-Ear Headphones**: While not strictly on-ear, these in-ear headphones are worth mentioning as they feature StayHear+ Ultra tips that rest gently on the ear canal opening rather than inside it, providing an on-ear-like experience for some users. They deliver rich, clear sound and have a secure, comfortable fit for extended listening sessions. The wired design ensures no battery concerns, and they come with an inline remote and microphone for controlling your music and taking calls.

Please note that Bose has discontinued certain on-ear models in recent years, such as the Bose SoundTrue Around-Ear II and the Bose On-Ear Headphones. However, you might still find them in the second-hand market or through authorized retailers with remaining stock.

If you're interested in purchasing a pair of Bose on-ear headphones, consider factors like noise cancellation needs, wireless connectivity preferences, battery life requirements, and budget. Additionally, make sure to try them on or read reviews about their fit, as comfort is crucial when it comes to on-ear headphones.