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ANTARES, a neutrino detector located in the depths of the Mediterranean Sea, operated successfully for over 15 years before being decommissioned in 2022. The telescope offered a vantage view of the Southern Sky and benefited from favourable water properties, enabling good angular resolution. This study makes use of data collected over the entire operational period of ANTARES to search for sources of high-energy cosmic neutrinos, considering both steady and flaring emission scenarios. First, a time-integrated search for high-energy neutrino clustering across much of the celestial sphere is conducted. The most significant accumulation is found at coordinates <inline-formula><mml:math><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>200</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>5</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mspace></mml:mspace><mml:mo>,</mml:mo><mml:mn>17</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>7</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> with a post-trial p value equal to 0.38. A dedicated search in the Galactic Plane is also performed for extended sources, yielding no significant excess. Additionally, a list of potential neutrino sources is investigated. The blazar MG3 J225517+2409 is identified as the most significant object, yet the excess remains compatible with background fluctuations. A mild local excess of 2.4<inline-formula><mml:math><mml:mi>σ</mml:mi></mml:math></inline-formula> is found for the blazar TXS 0506+056. The full sky is also examined for the presence of flaring neutrino emission. The most significant excess in this case corresponds to a <inline-formula><mml:math><mml:mo>∼</mml:mo></mml:math></inline-formula>4-day flare from the direction <inline-formula><mml:math><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>α</mml:mi><mml:mo>,</mml:mo><mml:mi>δ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>141</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>3</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mspace></mml:mspace><mml:mo>,</mml:mo><mml:mn>9</mml:mn><mml:mo>.</mml:mo><mml:msup><mml:mn>8</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, with a post-trial p-value of 0.30. Finally, the directions of sources highlighted in IceCube's time-dependent searches are investigated. Temporal overlaps between ANTARES and IceCube flares are identified for PKS 1502+106 and TXS 0506+056, with an estimated chance probability of about 0.02%. However, the absence of a corresponding strong signal in IceCube does not support an astrophysical interpretation of the temporal coincidence.